# Solution - UCSD Department of Physics

advertisement ```Problem 1
A man has +3.8 D lenses to provide full correction of his farsightedness. His old lenses
are +2.5 D.
(a) What is the near point for his unaided eyes?
(b) How far away from his eyes he must hold a paper to use his old lenses?
Solution:
(a) 3.8 = 1 / 0.25 + 1/ di =&gt; di = -5 m.
(b) 2.5 = 1 / do – 0.2 =&gt; do = 37 cm
Problem 2
Two rays A and B travel down a cylindrical optical fiber of diameter d  75m , length
l  1.0km , and index of refraction n1 = 1.465. Ray A travels a straight path down the
fiber’s axis, whereas ray B propagates down the fiber repeated reflections at the critical
angle each time it impinges on the fiber’s boundary. Determine the extra time t it takes
for ray B to travel down the entire fiber in comparison with
 ray A, assuming the fiber is
surrounded by a cylindrical glass “cladding” with index of refraction n2 = 1.46.

Solution:
t  t B  t A  l B v l A v  1 v(l A sin c  l A ) 

n1l A c(n1 n2 1)  1.7 10 8 s
Problem 3
A light ray is propagating in a crystal where its wavelength is 540 nm. It strikes the
interior surface of the crystal with an angle of 34 and emerges into the surrounding air
at 76 to the surface normal.
Find (a) the light frequency and (b) its wavelength in air.


Solution:

n2  sin 76 sin 34  1.74 .
f  c n2 2  3.2 1014 Hz .
The index of refraction of the crystal:
(a) Frequency of the light is
(b) 1  c f  937nm


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