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VISN1111(2013) Week 1

VISN1111 GEOMETRICAL AND PHYSICAL OPTICS 2013

TUTORIAL-1

1. A pencil of light diverges from a point source through a rectangular aperture 3 cm × 4 cm.

at 30 cm from the source. Find the area of the patch of light on a screen parallel to, and 120

cm from the aperture.  Ans. 300 sq.cm.

2. A person holds a circular aperture of diameter 25 mm at a distance 150 mm from his eye

and can just see the whole of a tree through the aperture. What is the angular size of the tree

(at the eye) and what is its height if the person is standing 75 m from the tree?

 Ans. 9.55°    , 12.5 m.

3. a) A pencil of light on passing through a lens of 40 mm diameter converges to a point

60 cm from the lens. Find the area of the cross section of the pencil at 20, 50 and

75 cm from the lens.  Ans. 5.59, 0.349, 0.785 sq.cm.

 b) Determine the vergence in the pencil of rays i) on leaving the lens. ii) at 20 cm from the

lens. iii) at 40 cm from the lens. iv) at 80 cm from the lens.  Ans. 1.67 D, 2.5 D, 5 D,−5 D

4. i) What is the vergence of light at a distance of 8 cm from a point source? At 42 cm? At 123

cm? ii) What is the vergence of converging light at a distance of 83 cm from the image

 point? At 32 cm? At 13 cm?  Ans. i) -12.5 D, -2.38 D, -0.81 D; ii) 1.2 D, 3.13 D, 7.69 D 

5. Given a -8.00 D diverging wavefront how far (in cm) is the wave from its point source?Calculate the same for a -6.00 D wavefront. Ans. 12.5 cm, 16.67 cm 

6. Given a +7.00 D converging wavefront, how far (in cm) is the image point? Calculate the

same for a +3.00 D wavefront?  Ans. 14.29 cm, 33.33 cm 

7. The light at position A has a vergence of +13.5 D. What is the vergence at position B, which

is 3 cm upstream from position A?  Ans. +9.61 D 

8. The light at position A has a vergence of -6.3 D. What is the vergence at position B which is

9 cm upstream from position A? Calculate the vergence at position C which is 37 cm

upstream from position A?  Ans. -14.55 D, +4.73 D

9. Calculate the number of waves from a point source S to a point ‘A’ 2 cm away for light at

wavelength 0.55 micrometre. Calculate the same for a point ‘B’ 2.5 cm away.

Are A and B in phase?  Ans. 36,363.636 waves ; 45,454.545 waves; No

10. A pinhole camera produces an image 2.25 cm tall, and when the screen is withdrawn

3 cm further from the pinhole the length of the image increases to 2.75 cm. What was the

original distance between the pinhole and the screen?  Ans. 13.5 cm

11. An object is 5 m from a pinhole. A screen is placed 12 cm behind the pinhole. When theobject is 2 m tall, what is the size of the image? What is the size of the image if the screen is

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VISN1111(2013) Week 1

moved closer, to a distance of 10 cm? What is the size of the image if the screen is moved

further, to a distance of 15 cm?  Ans. 4.8 cm, 4 cm, 6 cm. 

12. A piece of film 3 cm x 5 cm is placed 15 cm from a pinhole. What would be the linear field

of view of this pinhole in object space at a distance of 25 m from the pinhole? 

 Ans. 5 m x 8.33 m 

13. Red light, λ = 600 nm in vacuum, enters a glass block whereupon the wavelength reduces to

400 nm. Find the speed of light in the glass if the speed of light in vacuum is 3 x 108m/s.

Find the ratio of the speed of light in vacuum to the speed of light in glass.

 Ans. 2 x 108 m/s, 1.5.

14. A ray of light is incident upon a pond of water that is 2 m deep. If the angle of

incidence is 25º, by how many cm is the ray deviated when it reaches the bottom of the

 pond? Assume that the refractive index of water is 1.333.  Ans. 26.22 cm.

15. A parallel pencil of light is incident at an angle of 35° on the plane surface of a block of

glass of refractive index 1.523. Find the angle between the light reflected from the surface

and that refracted into the glass.  Ans. 122.88 °    

Some of these problems are from the book “Geometrical, Physical, and Visual Optics” - By

 Michael P. Keating