Question

# Find the coordinates of image of point object P in mm formed after two successive reflections one at concave mirror and the other at convex.

A
(+30 cm, 14 mm)
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B
(+30 cm, 7 mm)
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C
(+20 cm, 16 mm)
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D
(+20 cm, 14 mm)
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Solution

## The correct option is A (+30 cm, −14 mm)Reflection at concave mirror (M1): Object distance, u1=−20 cm Focal distance, f1=−15 cm Using mirror formula, 1v1+1u1=1f1 We get, 1v1=1−15+120 ⇒1v1=5−300 ⇒v1=−60 cm Magnification: m1=−v1u1 ⇒m1=−(−60)−20 ⇒m1=−3 Since, initially the height of the point P is h=2 mm, so the height at which the image point will be h′=|m1|×h ⇒h′=3×2 ⇒h′=6 mm Reflection at convex mirror (M2): The image formed by concave mirror acts as an object for convex mirror. So, object distance, u2=(+60−50)=+10 cm Focal length, f2 = +20 cm Using mirror formula: 1u2=1f2−1v2 ⇒1u2=120−110 ⇒1u2=−120 ∴v2=−20 cm Hence, the final position of image after two successive reflection at concave mirror and then at convex 20 cm in front of convex mirror, M2. Magnification: m2=−v2u2=−(−20)10=2 So, the image of the point will be formed above = m2 × (−6−2) =2×(−8) mm =−16 mm principal axis of m2 So, the coordinate point of the final image will be ((50+v2) cm,(−16+2) mm) =((50−20) cm,−14 mm) =(30 cm,−14 mm) Hence, option (a) is the correct answer. Why this question: To understand the image formation by combination of spherical mirrors.

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