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An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

A

30 cm towards the mirror

B

36 cm away from the mirror

C

30 cm away from the mirror

D

36 cm towards the mirror

Step-by-Step Solution

Sol. [Insert diagram of concave mirror with object O at 40 cm and focal length f = 15 cm]

1f=1v1+1u\frac{1}{f} = \frac{1}{v_1} + \frac{1}{u}

115=1v1140-\frac{1}{15} = \frac{1}{v_1} - \frac{1}{40}

1v1=115+140\Rightarrow \frac{1}{v_1} = \frac{1}{-15} + \frac{1}{40}

v1=24 cmv_1 = -24 \text{ cm}

When object is displaced by 20 cm towards mirror.

Now, u2=20u_2 = -20

1f=1v2+1u2\frac{1}{f} = \frac{1}{v_2} + \frac{1}{u_2}

115=1v2120\frac{1}{-15} = \frac{1}{v_2} - \frac{1}{20}

1v2=120115\frac{1}{v_2} = \frac{1}{20} - \frac{1}{15}

v2=60 cmv_2 = -60 \text{ cm}

So, image shifts away from mirror by =6024=36 cm= 60 - 24 = 36 \text{ cm}.

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