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Q.

With a concave mirror, an object is placed at a distance x1 from the principal focus, on the principal axis. The image is formed at a distance x2 from the principal focus. The focal length of the mirror is

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a

x1 x2

b

x1+x22

c

x1x2

d

x1 x2

answer is D.

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Detailed Solution

u=X1+f  ,    V=X2+ff=uVu+V⇒(x1+f)(x2+f)(x1+f)+(x2+f)f⇒x1x2+x1f+x2f+f2x1+x2+2f⇒x1f+x2f+2f2=x1x2+x1f+x2f+f2                      2f2−f2=x1x2∴f=x1x2
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