(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)
S safeer

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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