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  • (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 inci

(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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Safeer PP

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