# (a) Define the term ‘focal length of a mirror’. With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.(b) Calculate the angle of emergence (e) of the ray of light incident normally on the face AC of a glass prism ABC of refractive index . How will the angle of emergence change qualitatively, if the ray of light emerges from the prism into a liquid of refractive index 1.3 instead of air ?

a)

$\\\tan\theta=\frac{MC}{CD}\\\\\\tan2\theta=\frac{MD}{FD}$

$\\\text{for small }\theta\\\tan\theta=\theta\\\tan2\theta=2\theta \\\text{therefore}$

$\\\\\frac{MD}{FD}=2\frac{MC}{CD}\\FD=\frac{CD}{2}........(1)\\\text{for small}\ \theta\ FD=FP=f\\CD=CP=R\\From(1)\\F=R/2$

b)

$\\\sqrt{3}sin30=1.sine\\\sqrt{3}\times\frac{1}{2}=sine\\\\sine=\frac{\sqrt{3}}{2}\\\\e=60^{0}$

When the medium (the air) in which the prism is kept is replaced with a liquid
of refractive index 1.3 the angle of emergence would decrease. It is because bending in the ray of light will be lesser.

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