- When light strikes the boundary between two transparent media, it undergoes partial reflection and partial refraction.
- A ray passing from a rarer to a denser medium bends towards the normal, while one passing from a denser to a rarer medium bends away from the normal.
- The angles of incidence and refraction are generally unequal, causing light to bend.
- A ray incident normally (i = 0°) passes undeviated, even though its speed changes.
- Refraction occurs due to a change in the speed of light when it passes from one medium to another.
Definitions [19]
Definition: Ray Optics
A branch of optics that describes light propagation in terms of rays is called ray optics.
Definition: Refracted Light
Refracted light is the part of light enters into the other medium and travels in a straight path but in a direction different from its initial direction and is called the refracted light.
Definition: Refraction of Light
When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.
OR
Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.
OR
The bending of the light ray from its path in passing from one medium to the other medium is called 'refraction' of light.
OR
When a ray of light impinges on a polished, smooth, shiny surface, the rebounding of light within the same medium is called reflection of light.
Define the principal focus of a concave mirror.
Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.
Definition: Refraction
The change in the direction of the path of light when it passes from one transparent medium to another transparent medium is called refraction. The refraction of light is essentially a surface phenomenon.
or
When light passes from one transparent medium to another, its speed and direction change. This is called refraction.
Definition: Critical Angle
The angle of incidence in the denser medium corresponding to an angle of refraction of 90° in the rarer medium is called the critical angle.
Definition: Total Internal Reflection
The phenomenon where light rays are completely reflected back into a medium instead of being refracted into another medium is called total internal reflection.
or
Complete reflection of a ray of light at the interface of an optically denser medium and a rarer medium, back into the denser medium.
Define critical angle for a given medium.
When a ray of light propagates from a denser medium to a rarer medium, the angle of incidence for which the angle of refraction is 90° is called the critical angle.
Define the term ‘focal length of a mirror’.
When rays of light parallel to the principal axis of a mirror are incident on it, the rays after reflection either converge at a point or appear to diverge from a point. The distance of that point from the pole of the mirror is known as the focal length of the mirror.
Definition: Power of a Lens
The deviation of the incident light rays produced by a lens on refraction through it, is a measure of its power.
or
The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P.
OR
The power (P) of a thin lens is equal to the reciprocal of its focal length (f) measured in metres.
Define the power of a lens.
Power of a lens is defined as the ability of a lens to bend the rays of light. It is given by the reciprocal of focal length in metre.
The power of a lens is a measure of the deviation produced by it in the path of rays refracted through it.
Define and describe the magnifying power of an optical instrument.
Angular magnification or magnifying power of an optical instrument is defined as the ratio of the visual angle made by the image formed by that optical instrument (β) to the visual angle subtended by the object when kept at the least distance of distinct vision (α).
Definition: Telescope
An optical instrument that uses objective and eye piece lenses to magnify distant terrestrial or celestial objects is called a telescope.
Define the term ‘resolving power of a telescope’.
The resolving power of an astronomical telescope is defined as the reciprocal of the smallest angular separation between two point objects whose images can just be resolved by the telescope.
R.P = `(1.22 lambda)/D`
Resolving power is the ability of the telescope to distinguish clearly between two points whose angular separation is less than the smallest angle that the observer’s eye can resolve.
Definition: Telescope
An optical instrument used to observe distant objects by producing angular magnification is called a telescope.
Definition: Refractive Index
The ratio of the sine of the angle of incidence to the sine of the angle of refraction for a given pair of media is called refractive index.
Definition: Total Internal Reflection
The phenomenon in which a ray of light travelling from a denser to a rarer medium is completely reflected back into the denser medium when the angle of incidence exceeds the critical angle is called total internal reflection.
Definition: Refraction of Light
The change in direction of light when it passes obliquely from one transparent medium to another due to change in speed is called refraction of light.
Definition: Reflection of Light
The phenomenon in which light returns back into the same medium after striking a reflecting surface is called reflection of light.
Formulae [2]
Formula: Power of a Lens
Power of lens (in D) = \[\frac{1}{\text{focal length (in metre)}}\]
or
P = \[\frac {1}{f}\]
or
P = \[\frac {1}{f (m)}\]
Power of a Lens in a Medium:
P = (n2 - n1)\[\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\] = \[\frac {n_1}{f}\]
Formula: Magnifying Power of Telescope
- \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
- M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]
Theorems and Laws [2]
Law: Laws of Reflection
- The laws of reflection describe the behaviour of light when it strikes a reflecting surface.
- The first law states that the incident ray, the reflected ray and the normal drawn at the point of incidence all lie in the same plane.
- The second law states that the angle of reflection is always equal to the angle of incidence.
- These laws are valid for all reflecting surfaces, whether plane or curved. In the case of spherical mirrors, the normal at any point on the surface passes through the centre of curvature.
- The laws are independent of the nature of the reflecting material. Reflection also obeys the principle of reversibility of light. These two laws completely explain the phenomenon of reflection.
Law: Laws of Refraction (Snell’s Law)
- The laws of refraction describe the bending of light when it passes from one transparent medium to another.
- The first law states that the incident ray, refracted ray and the normal at the point of incidence lie in the same plane.
- The second law states that the ratio of sine of angle of incidence to sine of angle of refraction is constant for a given pair of media. This constant is called the refractive index.
- Mathematically, \[\frac{\sin i}{\sin r}=n_{21}\]
- The refractive index depends on the nature of the two media and the wavelength of light. If light travels from rarer to denser medium, it bends towards the normal. These two statements together are known as Snell’s law of refraction.
Key Points
Key Points: Sign Convention
- The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
- All distances parallel to the principal axis are measured from the pole of the mirror.
- All the distances measured to the right of the origin (along + x-axis) are taken as positive, while those measured to the left of the origin (along – x-axis) are taken as negative.
- Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
- Distances measured perpendicular to and below the principal axis (along the y-axis) are taken as negative.
Key Points: Focal Length of Spherical Mirrors
- Focal length = half of radius of curvature:\[f=\frac{R}{2}\]
- For concave mirror: f is negative (real focus).
- For convex mirror: f is positive (virtual focus).
- Focus of concave mirror = real point (reflected rays converge).
- Focus of convex mirror = virtual point (reflected rays appear to diverge).
Key Points: Refraction of Light
Key Points: Refraction at Spherical Surfaces
Convex lens: Thicker at the middle, thinner at the edges, converges parallel rays.
- Types: Double-convex, Plano-convex, Concavo-convex.
Concave lens: Thinner at the middle, thicker at the edges, diverges parallel rays.
- Types: Double-concave, Plano-concave, Convexo-concave.
Important Terms:
- Principal Axis: Straight line through the centres of curvature of two surfaces.
- Optical Centre (O): Ray passing through it goes undeviated with no lateral displacement.
- Principal Focus (F): Point where parallel rays converge (convex) or appear to diverge (concave) after refraction.
- Aperture: Effective diameter of light-transmitting area; Intensity ∝ (Aperture)²
Key Points: Refraction by a Lens
Lens Maker's Formula:
\[\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\]
Where:
- f = focal length, μ = refractive index of lens material
- R₁, R₂ = radii of curvature of the two surfaces
New Cartesian Sign Conventions for Lens:
- Distances measured from optical centre.
- Along incident light → positive; against incident light → negative.
- For convex lens: f is positive; for concave lens: f is negative.
Rules for Image Formation:
- Ray through optical centre → passes undeviated.
- Ray parallel to principal axis → passes through F₂ (convex) or appears to come from F₁ (concave).
- Ray towards/through first focus F₁ → emerges parallel to principal axis.
Key Points: Refraction of Light Through a Prism
- A prism is a transparent medium bounded by two polished plane surfaces inclined at an angle (< 90°).
- The angle between the refracting faces = Refracting angle (A).
- A ray of light undergoes two refractions passing through a prism.
Angle of Deviation:
δ = i1 + i2 − A or δ = i + e − A
Minimum Deviation (δmin):
- Occurs when i1 = i2 = i → ray passes symmetrically.
- At minimum deviation: \[r_1=r_2=r=\frac{A}{2}\]
- Minimum deviation: \[\delta_{min}=2i-A\]
- Angle of incidence at minimum deviation: \[i=\frac{A+\delta_{min}}{2}\]
Refractive Index of Prism:
\[\mu=\frac{\sin\left(\frac{A+\delta_{min}}{2}\right)}{\sin\left(\frac{A}{2}\right)}\]
Key Points: Optical Instruments
- An optical instrument uses the principles of optics to enhance, modify, or analyse light for specific purposes.
- They manipulate light through reflection, refraction, diffraction, or interference.
- Common instruments: simple microscope, compound microscope, telescope.
Key Points: Microscope and Its Types
Simple Microscope:
- Single convex lens used to magnify small objects (magnifying glass).
- Object placed between F and optical centre → Virtual, magnified, erect image.
Magnifying Power (MP):
| Condition | Formula |
|---|---|
| Image at infinity (relaxed eye) | \[MP=\frac{D}{f}\] |
| Image at least distance of distinct vision (D) | \[MP=1+\frac{D}{f}\] |
For larger magnification → focal length should be small.
Compound Microscope:
- Combination of two convex lenses for much larger magnification.
- Object placed between F and 2F of objective → real, inverted, magnified intermediate image.
- Intermediate image acts as object for eyepiece (simple microscope).
- Final image is virtual, inverted, and magnified.
Total Magnification:
MP = mo × me
Where:
-
\[m_o=\frac{v_o}{u_o}=\frac{L}{f_o}\] (L = tube length = distance between second focal point of objective and first focal point of eyepiece)
-
\[m_e=1+\frac{D}{f_e}\]
| Condition | Total MP | Tube Length |
|---|---|---|
| At least distance D | \[MP=\frac{L}{f_o}\left(1+\frac{D}{f_e}\right)\] | L = vo + ue |
| Relaxed eye (infinity) | \[MP=\frac{L}{f_o}\times\frac{D}{f_e}\] | L = vo + fe |
Properties for large magnification:
- Both fo and fe should be small.
- If tube length increases → magnifying power increases.
- fo is much smaller so objective is placed very near to principal focus.
Key Points: Telescope
Astronomical (Refracting) Telescope:
- Used to view distant objects.
- Objective lens (large focal length) forms image A'B' at its focus → acts as object for eyepiece.
- Eyepiece forms the final virtual, magnified image A''B''.
Magnifying Power: \[MP=\frac{\text{Visual angle with instrument}(\beta)}{\text{Visual angle for unaided eye}(\alpha)}\]
| Condition | Formula | Tube Length |
|---|---|---|
| Relaxed eye (normal adjustment) | \[m=-\frac{f_a}{f_c}\] | \[L=f_o+f_e\] |
| Distinct vision (D) | \[m=-\frac{f_o}{f_e}\left(1+\frac{f_e}{D}\right)\] | \[L=f_o+f_e\] |
Resolving Power of Telescope:
- Ability to produce distinct images of two closely spaced objects.
- Angular separation between two resolvable objects: \[\sin\theta=1.22\frac{\lambda}{d}\] (Rayleigh's criterion), where d = aperture.
- Resolving power is inverse of angular separation.
- Larger aperture → better resolving power.
Types of Telescope:
- Refracting telescope: Uses two convex lenses; large objective + small eyepiece.
- Reflecting telescope: Uses concave mirror to reflect light internally; secondary mirror directs to eyepiece.
- Keplerian telescope: Converging lens as eyepiece → inverted image.
- Galilean telescope: Diverging lens as eyepiece → erect image.
- Magnification of Refracting Telescope: \[M=\frac{f_{o}}{f_{e}}\]
Key Points:Magnifying Power of a Telescope
- The magnifying power of a telescope is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended by the object at the unaided eye.
- For an astronomical telescope in normal adjustment, \[m=\frac{f_o}{f_e}\]
- where fo is focal length of objective and fe is focal length of eyepiece. The objective has a large focal length and large aperture.
- The eyepiece has a small focal length. The final image is formed at infinity. The image formed is inverted. Greater the focal length of objective, greater is the magnifying power.
Key Points: Refraction Through a Prism
When light passes through a prism, it suffers deviation. The angle of deviation (δ) is given by
δ = i + e − A
At minimum deviation, the refracted ray inside the prism becomes parallel to its base. At this condition,
\[r_1=r_2=\frac{A}{2}\]
The refractive index of the prism is \[n=\frac{\sin\left(\frac{A+D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}\]
This relation is used to determine the refractive index experimentally. The angle of deviation depends on the angle of incidence.
Key Points: Lens Maker’s Formula
- The lens maker’s formula gives the focal length of a thin lens in terms of its refractive index and radii of curvature. It is expressed as \[\frac{1}{f}=(n_{21}-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\]
- It is derived by applying refraction at two spherical surfaces of the lens. The formula is valid for thin lenses. R₁ and R₂ are the radii of curvature of the two surfaces.
- The sign convention must be strictly followed. It is useful in designing lenses of required focal length. The formula applies to both convex and concave lenses.
Key Points: Refraction at a Spherical Surface
- When light passes through a curved interface separating two media, refraction occurs at a spherical surface.
- The relation between object distance (u), image distance (v), refractive indices (n₁ and n₂) and radius of curvature (R) is \[\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\]
- This relation is derived using geometrical approximation for small angles. It is valid for paraxial rays only.
- The Cartesian sign convention must be followed carefully. It applies to any curved refracting surface. This formula forms the basis for deriving the lens maker’s formula.
Key Points: Magnification by a Spherical Mirror
- Magnification is defined as the ratio of the height of the image to the height of the object. It also relates image distance and object distance.
- The magnification produced by a spherical mirror is given by \[m=\frac{h^{\prime}}{h}=-\frac{v}{u}\]
- A negative magnification indicates that the image is real and inverted. A positive magnification indicates that the image is virtual and erect.
- The magnitude of magnification indicates the size of the image relative to the object.
- The formula is valid for both concave and convex mirrors. Proper sign convention must be applied while solving problems.
Key Points: Thin Lens Formula
- The thin lens formula relates object distance, image distance and focal length of a thin lens. It is given by \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]
- It is valid for both convex and concave lenses. The formula holds for real as well as virtual images.
- It is derived from refraction at spherical surfaces. The Cartesian sign convention must be applied correctly. It is widely used in solving numerical problems related to lenses.
Key Points: Mirror Formula
- The mirror formula establishes a mathematical relationship between object distance (u), image distance (v) and focal length (f) of a spherical mirror.
- It is derived using geometrical relations and similar triangles formed by paraxial rays. The formula is expressed as \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\]
- It is valid for both concave and convex mirrors. The formula applies to real as well as virtual images. While using this formula, the Cartesian sign convention must be strictly followed.
- It simplifies numerical problems related to image formation by mirrors. This formula is fundamental in ray optics.
Key Points: Power of a Lens
- Power of a lens is defined as the reciprocal of its focal length in metres.
- It measures the ability of a lens to converge or diverge light rays. Mathematically, \[P=\frac{1}{f}\]
- The SI unit of power is dioptre (D). One dioptre is the power of a lens whose focal length is one metre.
- Convex lenses have positive power. Concave lenses have negative power. Greater the power, smaller is the focal length.
Important Questions [58]
- With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.
- Answer the Following Question. Under What Conditions is the Phenomenon of Total Internal Reflection of Light Observed? Obtain the Relation Between the Critical Angle of Incidence.
- A concave mirror of focal length 12 cm forms three times the magnified virtual image of an object. Find the distance of the object from the mirror.
- Three Lenses of Focal Length +10 Cm, —10 Cm and +30 Cm Are Arranged Coaxially as in the Figure Given Below. Find the Position of the Final Image Formed by the Combination.
- A Double Convex Lens is Made of a Glass of Refractive Index 1.55, with Both Faces of the Same Radius of Curvature. Find the Radius of Curvature Required, If the Focal Length is 20 Cm.
- Calculate the Speed of Light in a Medium Whose Critical Angle is 30° ?
- A ray of light passes through a prism of refractive index 2 as shown in the figure. Find: The angle of incidence (∠r2) at face AC. The angle of minimum deviation for this prism.
- Answer the following question. Under what conditions are total internal reflection possible? Explain it with a suitable example.
- The Figure Shows a Ray of Light Falling Normally on the Face Ab of an Equilateral Glass Prism Having Refractive Index`3/2`, Placed In Water of Refractive Index `4/3`
- State two conditions necessary for total internal reflection to occur.
- Write the Necessary Conditions for the Phenomenon of Total Internal Reflection to Occur ?
- Write the Relation Between the Refractive Index and Critical Angle for a Given Pair of Optical Media?
- One Day Chetan’S Mother Developed a Severe Stomach Ache All of a Sudden. She Was Rushed to the Doctor Who Suggested for an Immediate Endoscopy Test and Gave an Estimate of Expenditure for the Same.
- Define the critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.
- Define the term ‘focal length of a mirror’.
- A point object in the air is placed symmetrically at a distance of 60 cm in front of a concave spherical surface with a refractive index of 1.5. If the radius of curvature of the surface is 20 cm
- What Type of Wavefront Will Emerge from a (I) Point Source, and (Ii) Distance Light Source?
- Use the Above Relation to Obtain the Condition on the Position of the Object and the Radius of Curvature in Terms of N1and N2 When the Real Image is Formed.
- Answer the Following Question. an Optical Instrument Uses a Lens of 100 D for the Objective Lens and 50 D for Its Eye Piece. When the Tube Length is Kept at 20 Cm, the Final Image is Formed at Infinit
- A Double Convex Lens of + 5 D is Made of Glass of Refractive Index 1.55 with Both Faces of Equal Radii of Curvature. Find the Value of Its Radius of Curvature.
- In the given figure the radius of curvature of the curved face in the planoconvex and the planoconcave lens is 15 cm each. The refractive index of the material of the lenses is 1.5.
- You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
- An Equiconvex Lens of Focal Length 'F' is Cut into Two Identical Plane Convex Lenses. How Will the Power of Each Part Be Related to the Focal Length of the Original Lens ?
- What is meant by a power of a lens? Define its SI unit.
- How Does Focal Length of a Lens Change When Red Light Incident on It is Replaced by Violet Light? Give Reason for Your Answer.
- Define Power of a Lens. Write Its Units. Deduce the Relation 1 F = 1 F 1 + 1 F 2 for Two Thin Lenses Kept in Contact Coaxially.
- Find the Radius of Curvature of the Convex Surface of a Plano-convex Lens, Whose Focal Length is 0.3 M and the Refractive Index of the Material of the Lens is 1.5.
- An object is placed in front of a converging lens. Obtain the conditions under which the magnification produced by the lens is negative and positive.
- A point object is placed at O in front of a glass sphere as shown in figure. Show the formation of the image by the sphere.
- Explain the construction and working of a ‘Compound Microscope’.
- Draw a Labeled Ray Diagram to Obtain the Real Image Formed by an Astronomical Telescope in Normal Adjustment Position. Define Its Magnifying Power
- Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power.
- A Giant Refracting Telescope at an Observatory Has an Objective Lens of Focal Length 15 M. If an Eyepiece Lens of Focal Length 1.0 Cm is Used, Find the Angular Magnification of the Telescope.
- Write two important limitations of a refracting telescope over a reflecting-type telescope.
- Draw a Schematic Ray Diagram of a Reflecting Telescope Showing How Rays Coming from a Distant Object Are Received at the Eyepiece.
- Draw a Labelled Ray Diagram of an Astronomical Telescope to Show the Image Formation of a Distant Object.
- Draw a Labelled Ray Diagram of an Astronomical Telescope in the Near Point Adjustment Position. a Giant Refracting Telescope at an Observatory Has an Objective Lens of Focal Length 15 M
- "A Telescope Resolves Whereas a Microscope Magnifies." Justify this Statement ?
- Describe Briefly the Two Main Limitations and Explain How Far These Can Be Minimized in a Reflecting Telescope ?
- Write the Two Important Factors Considered to Increase the Magnifying Power?
- Draw a Ray Diagram Showing the Image Formation of a Distant Object by a Refracting Telescope ?
- Define the term ‘resolving power of a telescope’.
- State the Condition Under Which a Large Magnification Can Be Achieved in an Astronomical Telescope.
- You Are Given Three Lenses of Power 0.5 D, 4 D, and 10 D to Design a Telescope. Which Lenses Should Be Used as Objective and Eyepiece? Justify Your Answer.Why is the Aperture of the Objective Preferred to Be Large?
- Write Two Important Advantages Of Reflecting Telescope Over a Refracting Telescope.
- Draw a ray diagram of a refracting astronomical telescope when final image is formed at infinity. Also write the expression for its angular magnification (magnifying power).
- You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope ? Give reason
- With the help of a ray diagram explain the working of a reflecting telescope.
- Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.
- The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of 150 cm. Find the focal lengths of the two lenses.
- Draw a ray diagram depicting the formation of the image by an astronomical telescope in normal adjustment.
- Why Should the Objective of a Telescope Have Large Focal Length and Large Aperture? Justify Your Answer.
- Define Its Magnifying Power and Write the Expression for It?
- Define Magnifying Power of a Telescope. Write Its Expression.
- A Small Telescope Has an Objective Lens of Focal Length 150 Cm and an Eye Piece of Focal Length 5 Cm.If this Telescope is Used to View a 100 M High Tower 3 Km Away,
- How is the Working of a Telescope Different from that of a Microscope?
- Draw a Labeled Ray Diagram of a Reflecting Telescope. Mention Its Two Advantages Over the Refracting Telescope.
- The focal lengths of the objective and eyepiece of a microscope are 1.25 cm and 5 cm respectively.
Concepts [17]
- Ray Optics Or Geometrical Optics
- Reflection of Light by Spherical Mirrors
- Sign Convention for Reflection by Spherical Mirrors
- Focal Length of Spherical Mirrors
- Mirror Equation of Spherical Mirrors
- Refraction of Light
- Total Internal Reflection
- Applications of Total Internal Reflection
- Refraction at a Spherical Surfaces
- Refraction by a Lens
- Power of a Lens
- Combined Focal Length of Two Thin Lenses in Contact
- Refraction of Light Through a Prism
- Optical Instruments
- Microscope and it’s types
- Telescope
- Overview of Ray Optics and Optical Instruments
