# (a) When a convex lens of focal length 30 cm is in contact with a concave lens of focal length 20 cm, find out if the system is converging or diverging.(b) Obtain the expression for the angle of incidence of a ray of light which is incident on the face of a prism of refracting angle A so that it suffers total internal reflection at the other face. (Given the refractive index of the glass of the prism is $\mu$.)

Answers (1)

Given,

The focal length of the convex lens $(f_{1})=30\; cm$

The focal length of the concave lens $(f_{2})=20\; cm$

Now, the combined focal length $(f)$ will be ;

$\frac{1}{F}=\frac{1}{F_{1}}+\frac{1}{F_{2}}$

$\frac{1}{F}=\frac{1}{30}-\frac{1}{20}$             ($\because$ concave lens focal length =-20cm)

$\frac{1}{F}=\frac{-10}{600}$

$F=-60\; cm$

Hence, the combination works as a diverging lens since F is negative.

(b) To determine the angle of the incident ;

We know,

$\mu=\frac{1}{\sin i_{C}}$         (Where, $\mu =$ refractive prism)

Such that, $r_{1}+r_{2}=A$

$r_{1}=A-r_{2}\; \; \; \; \; (\because r_{2}=i_{C})$

$r_{1}=A-i_{C}$ ____(1)

Since, $\sin i_{1}=\mu \sin r_{1}$             (By refraction)

$\sin i_{1}=\mu \sin (A-i_{C})$            (From eqn (1))

$i_{1}=\sin ^{-1}\left \{ \mu \sin (A-i_{C}) \right \}$

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