Solutions of chapter 9. Ray Optics and Optical Instruments

1

A ray of light incident at an angle on a refracting face of a prism emerges from the other face normally. If the angle of the prism is 5° and the prism is made of a material of refractive index 1.5, the angle of incidence is

2

A short pulse of white light is incident from air to a glass slab at normal incidence. After travelling through the slab, the first colour to emerge is

3

An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The image

A. moves away from the lens with a uniform speed 5 m/s.

B. moves away from the lens with a uniform acceleration.

C. moves away from the lens with a non-uniform acceleration.

D. moves towards the lens with a non-uniform acceleration.

4

A passenger in an aeroplane shall

A. never see a rainbow.

B. may see a primary and a secondary rainbow as concentric circles.

C. may see a primary and a secondary rainbow as concentric arcs.

D. shall never see a secondary rainbow.

5

You are given four sources of light each one providing a light of a single colour – red, blue, green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is 90°. Which of the following statements is correct if the source of yellow light is replaced with that of other lights without changing the angle of incidence?

6

The radius of curvature of the curved surface of a Plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will

7

The phenomena involved in the reflection of radio waves by ionosphere is similar to

8

The direction of ray of light incident on a concave mirror is shown by PQ while directions in which the ray would travel after reflection is shown by four rays marked 1, 2, 3 and 4 (Fig 9.1). Which of the four rays correctly shows the direction of reflected ray?

9

The optical density of turpentine is higher than that of water while its mass density is lower. Fig 9.2. shows a layer of turpentine floating over water in a container. For which one of the four ray’s incident on turpentine in Fig 9.2, the path shown is correct?

10

A car is moving with at a constant speed of 60 km h^–1 on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h^–1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?

11

There are certain material developed in laboratories which have a negative refractive index (Fig. 9.3). A ray incident from air (medium 1) into such a medium (medium 2) shall follow a path given by

12

Consider an extended object immersed in water contained in a plane trough. When seen from close to the edge of the trough the object looks distorted because

13

A rectangular block of glass ABCD has a refractive index 1.6. A pin is placed midway on the face AB (Fig. 9.4). When observed from the face AD, the pin shall

14

Between the primary and secondary rainbows, there is a dark band known as Alexandra’s dark band. This is because

15

A magnifying glass is used, as the object to be viewed can be brought closer to the eye than the normal near point. This results in

16

An astronomical refractive telescope has an objective of focal length 20m and an eyepiece of focal length 2cm.

17

Will the focal length of a lens for red light be more, same or less than that for blue light?

18

The near vision of an average person is 25cm. To view an object with an angular magnification of 10, what should be the power of the microscope?

19

An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?

20

Three immiscible liquids of densities and refractive indices are put in a beaker. The height of each liquid column is. A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.

21

For a glass prism the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.

22

A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take

23

A circular disc of radius ‘R’ is placed co-axially and horizontally inside an opaque hemispherical bowl of radius ‘a’ (Fig. 9.5). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with transparent liquid of refractive index μ and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed?

24

A thin convex lens of focal length 25 cm is cut into two pieces 0.5 cm above the principal axis. The top part is placed at (0,0) and an object placed at (–50 cm, 0). Find the coordinates of the image.

25

In many experimental set-ups the source and screen are fixed at a distance say D and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.

26

A jar of height h is filled with a transparent liquid of refractive index μ (Fig. 9.6). At the center of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmetrically about the center, the dot is invisible.

27

A myopic adult has a far point at 0.1 m. His power of accommodation is 4 diopters. (i) What power lenses are required to see distant objects? (ii) What is his near point without glasses? (iii) What is his near point with glasses? (Take the image distance from the lens of the eye to the retina to be 2 cm.)

28

Show that for a material with refractive index light incident at any angle shall be guided along a length perpendicular to the incident face.

29

The mixture a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance d << h, the height of the column.

30

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by

Where r is the distance of the point of consideration from the center of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.

31

An infinitely long cylinder of radius R is made of an unusual exotic material with refractive index –1 (Fig. 9.7). The cylinder is placed between two planes whose normal are along the y direction. The center of the cylinder O lies along the y-axis. A narrow laser beam is directed along the y direction from the lower plate. The laser source is at a horizontal distance x from the diameter in the y direction. Find the range of x such that light emitted from the lower plane does not reach the upper plane.

32

(i) Consider a thin lens placed between a source (S) and an observer (O) (Fig. 9.8). Let the thickness of the lens vary as where b is the vertical distance from the pole. w₀ is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum; find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.