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Unformatted text preview: Problems: Week 13 Note: All solutions must have ray diagrams 13—1. 13~2. 13—3. 134. A penny lies at the bottom of a swimming pool which is 4m deep. What is the apparent
depth of the penny as viewed straight down if the refractive index of water is 1.33? The lens maker’s formula for a thin lens made of a material of refractive index n and
having two spherical surfaces of radii R F and R B is written as ' l 1 1
7“.‘”“”iR—;R7l How do you distinguish between a convergent lens and a divergent lens? [Hintz Use the
sign convention that distances measured along the path of light are positive and those
against the path of light are negative] Can you use a divergent lens to produce an image which is the same size as the object?
Justify your answer. A thin convergent lens (f = 20 cm) is placed on a plane mirror as shown. Where would
you place the object 0 so that the image coincides with itself? 0 135. An object is placed a distance of 5cm from a thin convergent lens whose focal length is
100m. Locate the image. (i) Is the image real or Virtual? (ii) What is the magniﬁcation? 136. A double convex lens is made of glass (n = 1.5). The surfaces have radii in the ratio 1:2.
If f = 6 cm, what are the radii? [Hintz Look at problem 13—2 again] 137. Newton had an unusual method for writing the lens equation 1 1 1
_+_=_ p q f
He measured the object and image distances from the focal point and wrote
x=p~f and x'=q—f
Show that this will lead to the lens equation
I xx'= f 2 : 138. The picture shows the paths of two raYs used to locate the image of a point object O. The
rays are paraxial (in the picture angles are slightly exaggerated), a << 1 , ,6 << 1. Show = h
that6 f. 13—9. 13—10. 1311. 13—12. l3~l3. Considering that the emission of light involves the transition of one electron in one atom,
explain why the phase of the light wave emitted by a simple lamp (not a laser) varies
randomly in time? ' ' When would you regard two sources of light to be incoherent? If light waves from two identical but incoherent sources are superposed we observe twice the intensity due to one source. Why? [Hintz ,(sin A + sin B) = 2 co s[ A H B j sin[ A + B] ] 2 2 What minimum path difference is needed to produce a phase shift of 7r radians in light of
wavelength 600nm? What would be the phase shift of 700nm light over this distance? Green light of wavelength 436nm is incident on a 580nm thick sheet of glass with
refractive index 1.5. What will be the phase difference between the wave reﬂected from
the top surface and that reflected from the bottom surface? ‘ 1344. Two coherent sources of 340Hz sound are 5m apart. (i) You are standing in the middle
(at 25111) and hear nothing (this is not a comment on your aural acuity). What does this
tell you about the phase difference of the two waves at their starting points? (ii) If the
speed of sound is 3401n/s how many such “quiet spots” (minima) will you encounter as
youwalk from one source to the other? ...
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 Fall '11
 Bhagat
 Physics, Light, convergent lens

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