Physics Ray Optics and Optical Instruments

A prism of refractive index n? and another prism of refractive index n? are stuck together (as shown in the figure). n? and n? depend on λ, the wavelength of light, according to the relation:
n? = 1.2 + (10.8 * 10?¹?)/λ² and n? = 1.45 + (1.8 * 10?¹?)/λ²
The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _______ nm.

A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index value of A is :

A ray of light entering from air into a denser medium of refractive index 4/3, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ should be equal to :

A ray of laser of a wavelength 630 nm is incident at an angle of 30° at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

The focal length f is related to the radius of curvature r of the spherical convex mirror by:

A point source of light S, placed at a distance 60cm infront of the centre of a plane mirror of width 50cm, hangs vertically on a wall. A man walks inform of the mirror along a line parallel to the mirror at a distance 1.2m from it (see in the figure). The distance between the extreme points where he can the image of the light source in the mirror is………….cm.

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R.

Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image.

Reason R : Magnification is achieved as the small object can be kept much closer to the eye that 25cm and hence it subtends a large angle.

In the light of the above statements, choose the most appropriate answer from the options given below:

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\overrightarrow{a},\overrightarrow{b}and\overrightarrow{c}$  respectively. Then choose the correct relation for these vectors.

 A short straight object of height 100cm lies before the central axis of a spherical mirror whose focal length has absolute value = 40cm. The image of object produced by the mirror is of height 25cm and has the same orientation of the object. One my conclude from the information

A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm . The magnifying power of telescope for viewing a distant object is: