  Difficult Conceptual Numericals

## Ray Optics And Optical Instruments

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1
Rotating plane mirrors:
Questions involving rotation of mirrors can be difficult at times. The very thing to remember is, if the plane mirror rotates by an angle , then the reflected ray rotates by an angle 2 in the same direction.
A flat mirror revolves at a constant angular velocity making revolutions per second. With what velocity (in ) will a light spot move along a spherical screen with a radius of metres, if the mirror is at the centre of curvature of the screen?
A
B
C
D
E
2
Combination of prism and mirror:
The total deviation of light in any combination can simply be found by the algebraic sum of the deviations produced by each optical element. For combination of prism and mirror, deviation produced by prism is added to the deviation produced by the mirror.
A prism having an apex angle of and refractive index of 1.50 is located in front of a vertical plane mirror as shown.A horizontal ray of light is incident on the prism. The total angle through which the ray is deviated is:

A
clockwise
B
clockwise
C
clockwise
D
clockwise
3
Finding refractive index of prism when angle of minimum deviation is given:
Sometimes, the angle of minimum deviation is not given. In fact, we will have to apply simple geometry to find the relation between the angle of prism A and angle of minimum deviation. There can be many layer to the question. Instead of asking the refracting index directly, the examiner might ask the factor by which light has slowed down in that medium, which is obviously, the R.I. of the medium.
A ray of light passing from air through an equilateral glass prism undergoes minimum deviation when the angle of incidence is th of the angle of prism. Calculate the speed of light in the prism.
4
An optical system immersed in a medium of given refractive index.
Usually, we come across questions where the optical systems are in placed in air. So using the absolute refractive indices for the lenses or prisms involved in place of relative R.I. doesn't make any difference. However we should be careful with equations where the system is immersed in an optical medium other than air.
A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be . What is the refractive index of the material of the prism? The refracting angle of the prism is . If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.
5
Compound microscope which has another combination of lenses:
In such questions, we use the very basic concepts step by step. We first reduce the combination to a single equivalent lens. And then use the results obtained for compound microscope for the final two lenses: the objective and the eyepiece.
A compound microscope is used to enlarge an object kept at a distance from it's objective which consists of several convex lenses in contact and has focal length . If a lens of focal length is removed from the objective, then by what distance the eye piece of the microscope must be moved to refocus the image
A
B
C
D