Refraction of light is the change in the path oflight as it passes obliquely from one transparent medium to another medium. According to law of refraction \(\frac{\sin i}{\sin r}={ }^{1} \mu_{2}\) where \({ }^{1} \mu_{2}\) is called refractive index of second medium with respect to first medium. From refraction at a convex spherical surface, we have \(\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}\) Similarly from refraction at a concave spherical surface when object lies in the rarer medium, we have \(\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}\) and when object lies in the denser medium, we have \(\frac{\mu_{1}}{v}-\frac{\mu_{2}}{u}=\frac{\mu_{1}-\mu_{2}}{R}\).
(i) Refractive index of a medium depends upon

(ii) A ray of light of frequency 5 x 10¹⁴ Hz is passed through a liquid. The wavelength of light measured inside the liquid is found to be 450 x 10^-9 m. The refractive index of the liquid is

(iii) A ray of light is incident at an angle of 60° on one face of a rectangular glass slab of refractive index 1.5. The angle of refraction is

(iv) A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distance of the virtual image from the surface of sphere is

(v) In refraction, light waves are bent on passing from one medium to the second medium because in the second medium

A compound microscope is an optical instrument used for observing highly magnified images of tiny objects. Magnifying power of a compound microscope is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended at the eye by the object, when both the final image and the object are situated at the least distance of distinct vision from the eye. It can be given that:\(m=m_{e} \times m_{o}\) where m_e is magnification
produced by eye lens and m_o is magnification produced by objective lens. Consider a compound microscope that consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm.
(i) The object distance for eye-piece, so that final image is formed at the least distance of distinct vision, will be

(ii) How far from the objective should an object be placed in order to obtain the condition described in part(i)?

(iii) What is the magnifying power of the microscope in case ofleast distinct vision?

(iv) The intermediate image formed by the objective of a compound microscope is

(v) The magnifying power of a compound microscope increases with

The lens maker's formula relates the focal length of a lens to the refractive index of the lens material and the radii of curvature of its two surfaces. This formula is called so because it is used by manufacturers to design lenses of
required focal length from a glass of given refractive index. If the object is placed at infinity, the image will be formed at focus for both double convex lens and double concave lens 
Therefore, lens maker's formula is \(\frac{1}{f}=\left[\frac{\mu_{2}-\mu_{1}}{\mu_{1}}\right]\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]\)
When lens is placed in air, \(\mu\) ₁ = 1 and \(\mu\)₂ = \(\mu\). The lens maker formula takes the form \(\frac{1}{f}=(\mu-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]\)
(i) The radius of curvature of each face of biconcave lens with refractive index 1.5 is 30 cm. The focal length of the lens in air is 

(ii) The radii of curvature of the faces of a double convex lens are 10 cm and 1.5 cm. If focal length is 12 cm, then refractive index of glass is 

(iii) An under-water swimmer cannot see very clearly even in absolutely clear water because of

(iv) A thin lens of glass (\(\mu\) = 1.5) offocallength 10 cm is immersed in water (\(\mu\) = 1.33). The new focal length is

(v) An object is immersed in a fluid. In order that the object becomes invisible, it should

A prism is a portion of a transparent medium bounded by two plane faces inclined to each other at a suitable angle. A ray of light suffers two refractions on passing through a prism and hence deviates through a certain angle from its original path. The angle of deviation of a prism is, \(\delta\) = (\(\mu\)- 1) A, through which a ray deviates on passing through a thin prism of small refracting angle A.
If \(\mu\) is refractive index of the material of the prism, then prism formula is,\(\mu=\frac{\sin \left(A+\delta_{m}\right) / 2}{\sin A / 2}\)
(i) For which colour, angle of deviation is minimum?

(ii) When white light moves through vacuum

(iii) The deviation through a prism is maximum when angle of incidence is

(iv) What is the deviation produced by a prism of angle 6°? (Refractive index of the material of the prism is 1.644).

(v) A ray of light falling at an angle of 50° is refracted through a prism and suffers minimum deviation. If the angle of prism is 60°, then the angle of minimum deviation is

An optical fibre is a thin tube of transparent material that allows light to pass through, without being refracted into the air or another external medium. It make use of total internal reflection. These fibres are fabricated in such a way that light reflected at one side of the inner surface strikes the other at an angle larger than critical angle. Even, if fibre is bent, light can easily travel along the length.

(i) Which of the following is based on the phenomenon of total internal reflection of light?

(ii) A ray of light will undergo rotal internal reflection inside the optical fibre, if it

(iii) If in core, angle of incidence is equal to critical angle, then angle of refraction will be

(iv) In an optical fibre (shown), correct relation for refractive indices of core and cladding is

(v) If the value of critical angle is 30° for total internal reflection from given optical fibre, then speed of light in that fibre is