- 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: Light
Light is an electromagnetic wave that travels in straight lines in a homogeneous medium.
-
Speed of light in vacuum: c = 3 × 10⁸ m/s.
Definition: Focal Length
The distance of the principal focus from the pole is called the focal length (f).
Definition: Image Distance
The distance of the image from the pole of the mirror is called the image distance (v).
Definition: Object Distance
In a spherical mirror, the distance of the object from its pole is called the object distance (u).
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: 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 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.
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.
Definition: Chromatic Aberration
The aberration that occurs due to the lens refracting different wavelengths of light at different angles, resulting in an image consisting of different colours without a single focussed image, is called chromatic aberration.
Definition: Spherical Aberration (Lens)
The aberration caused by the spherical shape of the lens, where light rays at the edges focus at a different point than those near the centre, leading to a blurred image, is called spherical aberration.
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.
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: 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.
Formulae [8]
Formula: Mirror Formula
\[\frac {1}{v}\] + \[\frac {1}{u}\] = \[\frac {1}{f}\]
Formula: Magnification
Magnification (m) = \[\frac{\text{Height of the image (}h'\text{)}}{\text{Height of the object (}h\text{)}}\] = \[\frac {h'}{h}\]
Magnification in terms of object and image distances:
Magnification (m) = \[\frac {h'}{h}\] = -\[\frac {v}{u}\]
Formula: Refractive Index
n = \[\frac {\text {sin i}}{\text {sin r}}\] = \[\frac {c}{v}\] = \[\frac {\text {Real depth}}{\text {Apparent depth}}\]
Formula: Apparent Depth (Glass Slab)
d = t - \[\frac {t}{μ}\] = t\[\left(1-\frac{1}{\mu}\right)\]
Formula: Magnifying Power of Telescope
- \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
- M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]
Formula: Lens Formula
\[\frac {1}{v}\] - \[\frac {1}{u}\] = \[\frac {1}{f}\]
Formula: Lens Magnification
Magnification (m) = \[\frac{\text{Height of the Image}}{\text{Height of the object}}=\frac{h^{\prime}}{h}\]
Magnification in terms of object and image distances:
Magnification (m ) = \[\frac {h'}{h}\] = \[\frac {v}{u}\]
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)\[\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\] = \[\frac {n_1}{f}\]
Theorems and Laws [2]
Law: Laws of Reflection
- The angle of reflection is equal to the angle of incidence.
- The incident ray, the reflected ray, and the normal lie in the same plane.
- The incident ray and the reflected ray are on opposite sides of the normal.
Law: Laws of Refraction
-
First Law: Incident ray, refracted ray, and normal to the interface at the point of incidence all lie in the same plane.
-
Second Law (Snell's Law): \[\frac{\sin i}{\sin r}=\mathrm{constant}=\frac{\mu_2}{\mu_1}\]
Extended Snell's Law: \[\frac{\sin i}{\sin r}=\frac{\mu_2}{\mu_1}=_1\mu_2=\frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}\]
Key Points
Key Points: Image Formation by Concave Mirror
| No. | Object Position | Image Position | Nature of Image | Size of Image |
|---|---|---|---|---|
| 1 | At infinity | At focus (F) | Real, Inverted | Highly diminished (point-sized) |
| 2 | Beyond centre of curvature (C) | Between F and C | Real, Inverted | Diminished |
| 3 | At centre of curvature (C) | At centre of curvature (C) | Real, Inverted | Same size as object |
| 4 | Between C and F | Beyond C | Real, Inverted | Enlarged (magnified) |
| 5 | At focus (F) | At infinity | Real, Inverted | Highly enlarged (very large) |
| 6 | Between focus (F) and pole (P) | Behind the mirror | Virtual, Erect | Enlarged (magnified) |
Key Points: Image Formation by a Convex Mirror
| No. | Object Position | Image Position | Nature of Image | Size of Image |
|---|---|---|---|---|
| 1 | At infinity | At focus (F), behind the mirror | Virtual, Erect | Highly diminished (point-sized) |
| 2 | Between infinity and pole (P) | Between F and P, behind the mirror | Virtual, Erect | Diminished |
Key Points: Sign Convention
- Pole (mirror) or optical centre (lens) is the origin; principal axis is the X-axis.
- Distances to the right are positive, to the left are negative; heights above the axis are positive, below are negative.
- Concave mirror: and R are negative; Convex mirror: and R are positive.
- Real images: image distance and magnification are negative; Virtual images: both are positive.
- Lenses are always negative; they are positive for real images and negative for virtual images; they are positive for convex lenses and negative for concave lenses.
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: Thin Lenses and Their Combination
Lens Formula:
\[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]
Magnification:
\[m=\frac{h_i}{h_o}=\frac{v}{u}=\frac{f}{f+u}=\frac{f-v}{f}\]
Combination of Thin Lenses in Contact:
- Effective focal length: \[\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+...\]
- Total power: P = P1 + P2 + P3 + ...
- When one lens is concave and other convex: \[F=\frac{f_1f_2}{f_2-f_1}\]
For Separated Lenses (distance d apart):
\[\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}\]
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: \[M=\frac{f_{o}}{f_{e}}\]
Concepts [21]
- Fundamental Concepts of Light
- Reflection of Light by Spherical Mirrors
- Image Formation by Concave Mirror
- Image Formation by a Convex Mirror
- Sign Convention
- Focal Length of Spherical Mirrors
- Ray Optics - Mirror Formula
- Refraction of Light
- Total Internal Reflection
- Refraction at a Spherical Surface and Lenses
- Refraction at a Spherical Surfaces
- Refraction by a Lens
- Thin Lenses and Their Combination
- Refraction of Light Through a Prism
- Optical Instruments
- Microscope and it’s types
- Telescope
- Law of Reflection of Light
- Laws of Refraction
- Lens Formula
- Power of a Lens
