Question

If the velocity of light in water is $2.25\times {10}^{10}cm$ per second and that is glass is $2\times {10}^{10}cm$ per second. A slab of this glass is immersed in water, what will be the critical angle of incidence of a ray of light tending to go from glass slab to water ?

• A. ${\sin }^{-1}3/5$
• B. ${\sin }^{-1}8/9$
• C. ${\sin }^{-1}4/5$
• D. ${\sin }^{-1}3/4$

Answer 1

The correct option is B ${\sin }^{-1}8/9$

given,

velocity of light in water $v_w=2.25\times {10}^{10}cm/s$

velocity of light in glass $v_g=2\times {10}^{10}cm/s$

refractive index of glass w.r.t water =${}_w{\mu }_g=\frac{velocityoflightinwater}{velocityoflightinglass}=\frac{2.25\times {10}^{10}}{2\times {10}^{10}}=\frac{9}{8}$

refractive index of water w.r.t. glass =${}_g{\mu }_w=\frac{1}{{}_w{\mu }_g}=\frac{8}{9}$

let the critical angle be $\angle i_c$

then $sin{i}_c=\frac{1}{{}_w{\mu }_g}{=}_g{\mu }_w$

$sin{i}_c=\frac{8}{9}\angle i_c={sin}^{-1}\left(\frac{8}{9}\right)$

Option B is correct.