Ray Optics and Optical Instruments

### (i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle 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.(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.β = √(n-1)k1 u/v / u + v

i) Time taken by the ray to travel from S to P1 is = t1 = √u2 + b2/c Time taken by the ray to travel from P1 to O is = t2 = v/c (1+ ½ b2/v2) Time taken to travel through the lens is =...

### Show that for a material with refractive index µ ≥ 2 , light incident at any angle shall be guided along a length perpendicular to the incident face. Answer:

Let the refractive index of the rectangular slab be μ ≥ √2. μ = 1/sin ic sin ic > 1/ μ cos r ≥ 1/ μ sin i/sin r = μ From Snell’s law Sin I = μ sin r i = 90o 1 + 1 ≤ μ2 2 ≤ μ2 Taking the square...

### A jar of height h is filled with a transparent liquid of refractive index µ. At the centre 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 centre, the dot is invisible.

tan ic d/2/h ic = d/2h d = 2h tan ic d = 2h ×1/√μ2 – 1

### 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 L << |v-f|

The mirror formula is 1/v + 1/u = 1/f u is the object distance v is the image distance du = |u1 – u2| = L Differentiating on the both sides we get, dv/v2 = -du/u2 v/u = f/u-f du = L, therefore,...

### For a glass prism (µ = √3 ) the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.

μ = sin[(A + δm)/2]/sin (A/2)

### An astronomical refractive telescope has an objective of focal length 20m and an eyepiece of focal length 2cm.(a) The length of the telescope tube is 20.02m. (b) The magnification is 1000. (c) The image formed is inverted. (d) An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.

Answer: (a) The length of the telescope tube is 20.02m. (b) The magnification is 1000. (c) The image formed is inverted.                      ...

### 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(a) a larger angle to be subtended by the object at the eye and hence viewed in greater detail.(b) the formation of a virtual erect image.(c) increase in the field of view.(d) infinite magnification at the near point.

Answer: (a) a larger angle to be subtended by the object at the eye and hence viewed in greater detail. (b) the formation of a virtual erect image.              ...

### Between the primary and secondary rainbows, there is a dark band known as Alexandar’s dark band. This is because(a) light scattered into this region interfere destructively.(b) there is no light scattered into this region(c) light is absorbed in this region.(d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and 50°.

Answer: (a) light scattered into this region interfere destructively. (d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and...

### A rectangular block of glass ABCD has a refractive index 1.6. A pin is placed midway on the face AB. When observed from the face AD, the pin shall (a) appear to be near A.(b) appear to be near D.(c) appear to be at the centre of AD.(d) not be seen at all.

Answer: (a) appear to be near A. (d) not be seen at all. The pin will appear to be near A as long as the angle of incidence on AD of the ray emerging from the pin is smaller...

### 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(a) the apparent depth of the points close to the edge is nearer the surface of the water compared to the points away from the edge.(b) the angle subtended by the image of the object at the eye is smaller than the actual angle subtended by the object in the air.(c) some of the points of the object far away from the edge may not be visible because of total internal reflection.(d) water in a trough acts as a lens and magnifies the object.

Answer: (a) the apparent depth of the points close to the edge is nearer the surface of the water compared to the points away from the edge. (b) the angle subtended by the image of the object at the...

### A car is moving with at a constant speed of 60 km h–1 on a straight road. Looking at the rearview 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 still the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?(a) The speed of the car in the rear is 65 km h–1.(b) In the side mirror, the car in the rear would appear to approach with a speed of 5 km h–1 to the driver of the leading car.(c) In the rearview mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.(d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

Answer: (d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

### The optical density of turpentine is higher than that of water while its mass density is lower. The figure shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in the figure, the path shown is correct?a) 1b) 2c) 3d) 4

Answer: b) 2 When light travels from (optically) rarer medium air to optically denser medium turpentine, it bends towards the normal, i.e., θ1 >...

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

Answer: b) 2 After reflection, the ray PQ of light that passes through focus F and strikes the concave mirror should become parallel to the primary...

### The phenomena involved in the reflection of radiowaves by ionosphere is similar toa) reflection of light by a plane mirrorb) total internal reflection of light in the air during a miragec) dispersion of light by water molecules during the formation of a rainbowd) scattering of light by the particles of air

Answer: b) total internal reflection of light in the air during a mirage The ionosphere, a layer of the atmosphere, reflects radio waves, allowing them to reach far-flung portions of the globe....

### 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 willa) act as a convex lens only for the objects that lie on its curved sideb) act as a concave lens only for the objects that lie on its curved sidec) act as a convex lens irrespective of the side on which the object liesd) act as a concave lens irrespective of the side on which the object lies

Answer: c) act as a convex lens irrespective of the side on which the object lies

### A passenger in an aeroplane shalla) never see a rainbowb) may see a primary and a secondary rainbow as concentric circlesc) may see a primary and a secondary rainbow as concentric arcsd) shall never see a secondary rainbow

Answer: b) may see a primary and a secondary rainbow as concentric circles As an aeroplane flies higher in the sky, passengers may notice a primary and secondary rainbow in the form of concentric...