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Ray Optics and Optical Instruments

An infinitely long cylinder of radius R is made of an unusual exotic material with refractive index –1. The cylinder is placed between two planes whose normals are along the y-direction. The centre 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.

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The refractive index of the cylinder is -1 and is placed in the air of μ = 1 AB is incident at B to the cylinder such that θr will be negative θ1= θi = θr Total deviation of the outcoming ray is...

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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 n(r) = 1 + 2 GM/rc2 where r is the distance of the point of consideration from the centre 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.

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n(r) = 1 + 2GM/rc2

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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 deviates from its original path. Find the deviation in travelling a horizontal distance d << h, the height of the column.

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Let the height of the long vertical column with transparent liquid be h and dx be the thickness The angle at which the ray AB enters is θ Let y be the new height of the liquid (θ + d θ) is the...

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A myopic adult has a far point at 0.1 m. His power of accomodation 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.)

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i) Power lenses are required to see distant objects 1/f = 1/v – 1/u 1/f = 1/10 f = -10 cm = -0.1 m P = 1/f P = 1/(-0.1) P = -10 diopter ii) When no corrective lens used Pn = Pf + Pa u = -10 cm =...

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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.

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u = -x1 v = +(D – x1) 1/D – x1 – 1/(-x1) = 1/f u = -x2 v = +(D – x2) 1/D – x2 – 1/(-x2) = 1/f D = x1 + x2 d = x2 – x1 x1 = D – d/2 D – x1 = D + d/2 u = D/2 + d/2 v = D/2 – d/2 m1 = D – d/D + d m2/m1...

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A circular disc of radius ‘R’ is placed co-axially and horizontally inside an opaque hemispherical bowl of radius ‘a’. 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?

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        Distance at which the bowl should be placed in the disc is given as: d = μ(a2 – b2)/√(a + r)2 – μ(a – r)2

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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 90o. 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?
a) the beam of red light would undergo total internal reflection
b) the beam of red light would bend towards normal while it gets refracted through the second medium
c) the beam of blue light would undergo total internal reflection
d) the beam of green light would bend away from the normal as it gets refracted through the second medium

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Answer: c) the beam of blue light would undergo total internal reflection

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A ray of light incident at an angle θ on a refracting face of a prism emerges from the other face normally. If the angle of the prism is 5o and the prism is made of a material of refractive index 1.5, the angle of incidence is
a) 7.5o
b) 5o
c) 15o
d) 2.5o

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Answer: a) 7.5o The distance between the refracting surfaces is negligible with thin prisms, thus the prism angle (A) is very small. Because A = r1 + r2, if A is tiny, both r1 and r2 will be little...

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Figure below shows a biconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

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Answer – According to the question –  Focal length of the given convex lens is f1 = 30 cm Since, the liquid acts as a mirror. Focal length of the liquid is denoted by f2 Total focal length...

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Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in Fig. 9.36. A current in the coil produces a deflection of 3.5° of the mirror. What is the displacement of the reflected spot of light on a screen placed 1.5 m away?

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Answer – According to the question –  Angle of deflection is θ = 3.5° The distance of the screen from the mirror is D = 1.5 m The deflection undergone by the reflected rays are twice the angle...

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A Cassegrain telescope uses two mirrors as shown in Fig. 9.33. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?

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Answer - Below is the diagram of a Cassegrain telescope. It has a concave and a convex mirror. We are given – Distance between the secondary mirror and the objective mirror is d = 20 mm Radius of...

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The virtual image of each square in the figure is to have an area of 6.25 mm2. Find out, what should be the distance between the object in Exercise 9.30 and the magnifying glass?If the eyes are too close to the magnifier, would you be able to see the squares distinctly?

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Answer – According to the question – Area of the virtual image of each square is A = 6.25 mm2 Area of each square is A0 = 1 mm2 Hence, the linear magnification of the object can be determined...

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A person looking at a cloth with a pattern consisting of vertical and horizontal lines is able to see the vertical lines more distinctly than the horizontal ones. What is this defect due to? How is such a defect of vision corrected?

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Answer – The person in the circumstance is having trouble seeing the horizontal lines, but the vertical lines are clearly apparent. When the eye's refracting system does not work in the same way for...

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For a normal eye, the far point is at infinity and the near point of distinct vision is about 25cm in front of the eye. The cornea of the eye provides a converging power of about 40 dioptres, and the least converging power of the eye-lens behind the cornea is about 20 dioptres. From this rough data estimate the range of accommodation (i.e., the range of converging power of the eye-lens) of a normal eye.

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Answer: We have –Least distance of distinct vision is d = 25 cmFar point of a normal eye is d’ = ∞Converging power of the cornea is $P_{c}=40D$Least converging power of the given eye-lens is...

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You are given prisms made of crown glass and flint glass with a wide variety of angles.
Suggest a combination of prisms which will
(i) deviate a pencil of white light without much dispersion,
(ii) disperse (and displace) a pencil of white light without much deviation.

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Answer - (i) The two prisms must be in close proximity to one another. The bases of these two prisms must be on opposite sides of the white light that is incident. White light is dispersed for the...

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(i) Figure below shows a cross-section of a ‘light pipe’ made of a glass fiber of refractive
index 1.68. The outer covering of the pipe is made of a material of refractive index
1.44. What is the range of the angles of the incident rays with the axis of the pipe
for which total reflections inside the pipe take place, as shown in the figure.
(ii) What is the answer if there is no outer covering of the pipe?

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Answer – (i) Refractive index of the glass fibre is = $\mu_{2}$= 1.68 Refractive index of the outer covering of thr pipe is = $\mu_{1}$= 1.44Angle of incidence is iAngle of refraction is rAngle...

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A small pin fixed on a tabletop is viewed from above from a distance of 50 cm. By
what distance would the pin appear to be raised if it is viewed from the same point
through a 15 cm thick glass slab held parallel to the table? Refractive index of glass =
1.5. Does the answer depend on the location of the slab?
Answer:

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According to the question,The actual depth of the pin is d = 15 cmApparent depth of the pin is = d’Refractive index of glass is $\mu$=1.5 here, the ratio of actual depth to the apparent depth and...

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A person with a normal near point (25 cm) using a compound microscope with objective of focal length 8.0 mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0 mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope,

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Answer: According to the question, Focal length of the given objective lens is $ f_{o}$= 8 mm = 0.8 cm Focal length of the eyepiece is $ f_{e}$= 2.5 cm Object distance for the given objective lens...

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A compound microscope consists of an objective lens of focal length 2.0cm and an eyepiece of focal length 6.25cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25 cm), and (b) at infinity? What is the magnifying power of the microscope in each case?

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Answer: According to the question, we have – Focal length of the given objective lens is f1=2.0 cm Focal length of the given eyepiece is f2=6.25 cm Distance between the eyepiece and the objective...

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A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?

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Answer : According to the question, the object given is virtual and the image formed is real. Object distance is u= +12 cm (i) The focal length of the convex lens is f =20 cm Image distance is...

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A prism is made of glass of unknown refractive index. A parallel beam of light is incident on the face of the prism. The angle of minimum deviation is measured to be 40°. What is the refractive index of the
material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.

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Answer: We are given that – Angle of minimum deviation is  $\delta_{m}=40°$ Angle of the prism is  A = $60°$ Refractive Index of water is given by, $\mu=1.33$ Material’s refractive Index =...

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A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)

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Answer : We are given the following information – Bulb’s actual depth in water is d1=80 cm =0.8 m Refractive Index of water is $\mu$= 1.33 I is the Angle of incidence r is the Angle of refraction –...

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The figures above show the refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence
in water is 45° with the normal to a water-glass interface.

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For the glass-air interface, we are given that – Angle of incidence is i =60° Angle of refraction is r=35° Using Snell’s law, the refractive index of the glass with respect to air becomes –...

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A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If
water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

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Answer: We are given that Actual depth of the needle in water here is h1=12.5cm Apparent depth in water is h2 =9.4 cm Refractive Index of water is given by – $\mu$ The value of $\mu$ can be...

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A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

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Answer – We are given that, Height of the candle is h =2.5 cm Let the image size be h’ Object distance is u = -27 cm Radius of the concave mirror, is R = -36 cm Focal length of the concave mirror...

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