A convex lens of focal length 20 , cm and a c | vedclass

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(D) For a system to output a parallel beam from an incident parallel beam,the final image must be at infinity.$1$. The parallel beam incident on the c

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$-15$

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(D) For a system to output a parallel beam from an incident parallel beam,the final image must be at infinity.$1$. The parallel beam incident on the convex lens $(f_1 = 20 \, cm)$ focuses at its focal point,which is $20 \, cm$ behind the lens.$2$. The concave mirror is placed $5 \, cm$ behind the lens. Therefore,the distance of the focal point of the lens from the mirror is $20 \, cm - 5 \, cm = 15 \, cm$.$3$. For the light to emerge parallel from the mirror,the light must be incident on the mirror such that it appears to come from its focal point (or the object is at the focal point). Since the rays are converging towards a point $15 \, cm$ in front of the mirror,this point must be the focal point of the concave mirror.$4$. Thus,the focal length $f$ of the concave mirror is $15 \, cm$. Since it is a concave mirror,by sign convention,$f = -15 \, cm$.

$A$ convex lens of focal length $20 \, cm$ and a concave mirror of focal length $f$ are placed coaxially at a distance of $5 \, cm$ apart. $A$ parallel beam of light incident on the convex lens emerges from the system as a parallel beam. Then $f = \dots \, cm$.

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