Overview of Ray Optics and Optical Instruments

The phenomenon in which light returns back into the same medium after striking a reflecting surface is called reflection 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.

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.

An optical instrument used to observe distant objects by producing angular magnification is called a telescope.

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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

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.

• 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 f_o is focal length of objective and f_e​ 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.