First slide

Ray optics

Question

Two parallel rays, one of red light and the other of violet light, are incident on the flat end of a 2m long glass rod. Wavelength of violet light in vacuum is 4000 $\overset{o}{A}$ and that of red light is 7000 $\overset{o}{A}$ . The mean refractive index of glass is 1.5 then number of waves of violet light in the rod exceeds the number of waves of red light by

Moderate

A

60%
B

75%
C

25%
D

30%

Solution

If l be the actual length of rod, then number of waves $n = \frac{l}{(λ / μ)} = \frac{μl}{λ}$
$∴$ Percentage increase $= \frac{n_{V} - n_{R}}{n_{R}} = \frac{μl (\frac{1}{λ_{V}} - \frac{1}{λ_{R}})}{μl / λ_{R}} \times 100 %$
$= (\frac{λ_{R}}{λ_{V}} - 1) \times 100 % = (\frac{7}{4} - 1) \times 100 % = 75 %$

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