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Question: A small piece of wire bent into an L shape with upright and horizontal portions of equal lengths, is...

A small piece of wire bent into an L shape with upright and horizontal portions of equal lengths, is placed with the horizontal portion along the axis of the concave mirror whose radius of curvature is 10 cm. If the bend is 20 cm from the pole of the mirror, then the ratio of the lengths of the images of the upright and horizontal portions of the wire is –

A

1 : 2

B

3 : 1

C

1 : 3

D

2 : 1

Answer

3 : 1

Explanation

Solution

Focal length of mirror f = 102\frac { 10 } { 2 } = 5 cm

Part PQ ® transverse magnification

length of image L1 = (ff−u)\left( \frac { f } { f - u } \right) × L0

= [−5−5−(−20)]\left[ \frac { - 5 } { - 5 - ( - 20 ) } \right] L0­ = –

For part QR : – longitudinal magnification

length of image L2 = (ff−u)2\left( \frac { f } { f - u } \right) ^ { 2 } L0 =

So = 31\frac { 3 } { 1 }