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Q.

As shown in figure an object "O" is at the position (–10, 2) with respect to origin "P". The concave mirror M₁ has radius of curvature 30 cm. A place mirror M₂ is kept at a distance of 40 cm in front of concave mirror. Considering first reflection at concave mirror M₁ and second through plane mirror M₂. Find the co-ordinates of second image w.r.t. origin P

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a

–40, –70

b

–52, –70

c

– 46, –70

d

–52, – 60

answer is C.

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Detailed Solution

$For M_{1} : \begin{aligned} u = - 10 cm \end{aligned}$
$\begin{array}{r} f = - 15 cm \\ n_{0} = 2 \end{array}$
Using mirror formula v = 30 cm
and n_I = 6 cm
The image formed by plane mirror is at 70 cm below the principle axis and 70 + 6 – 30 = 46 cm
from concave mirror.
So, coordinates of second image w.r.t.
P = (– 46, – 70)

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