Question

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$, a ray incident at an angle $\theta$, on the face AB would get transmitted through the face AC of the prism provided

• A. $\theta >si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
• B. $\theta <si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
• C. $\theta >co{s}^{-1}\left[\mu sin(A+si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
• D. $\theta <co{s}^{-1}\left[\mu sin(A+si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$

Answer 1

Answer: (A)

Consider refraction though AB surface

Using Snell's law,

$1\sin \theta =\mu \sin r$...(i)

Now for ray to transmit through AC the angle of incidence should be less the

critical angle

i.e. $r^{\prime }<{\sin }^{-1}\frac{1}{\mu }$

From triangle APQ$A+{90}^{\circ }-r+{90}^{\circ }-r^{\prime }=180$

$r^{\prime }=A-r;$ $A-r<{\sin }^{-1}\frac{1}{\mu }$

From equation (i)

$\theta >si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$

Option A is correct.