Question

(a) Monochromatic light of wavelength 589 nm is incident from air on a water surface. If p for water is 1.33, find the wavelength, frequency and speed of the refracted light.
(b) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.

Answer 1

Given : $\mu =1.33$
${\lambda }_a=589nm$
As $\mu =\frac{c}{v}$
v = $\frac{c}{\mu }=\frac{3\times {10}^8}{1.33}$
Speed, v = $2.26\times {10}^{8}m/s$
As the frequency remains same,
$\therefore$ v = $\frac{c}{{\lambda }_a}=\frac{3\times {10}^8}{589\times {10}^{-9}}$
Frequency v = $5.09\times {10}^{14}Hz$
Wavelength, ${\lambda }_w=\frac{v}{\nu }$
= $\frac{2.26\times {10}^8}{5.09\times {10}^{14}}$
= 444 nm
(b) Given : $\mu =1.55,f=20cm$
We know that ,
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})\frac{1}{20}=(1.55-1)(\frac{1}{R}+\frac{1}{R})\frac{1}{20}=0.55\times \frac{2}{R}R=20\times 0.55\times 2R=22cm$