Question

An object is shifted from the center of curvature of a concave mirror of focal length 25 cm , by 5cm towards the pole. Find the displacement of the imaage

Answer 1

Given : –

• An object is shifted 5 cm towards the pole from the centre of curvature of a concave mirror .
• Focal length of the mirror is 25 cm .

To Find : –

• The displacement of the image .

Solution : –

As given focal length of the mirror is 25 cm .

So, accordingly the centre of curvature will be

⪼ C = 2R

⪼ C = 2 × 25

⪼ C = 50 cm

The object is shifted 5 cm towards the pole, means object distance will be

⪼ u = 50 – 5

⪼ u = 45 cm

⪼ u = – 45 cm [ concave mirror ]

Now, from mirror formula : –

$\boxed{ \sf{ \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} }}$

$\rightarrow \: \sf{ \dfrac{1}{- 25} = \dfrac{1}{v} + \dfrac{1}{ - 45} } \\ \\ \rightarrow \: \sf{ \dfrac{1}{v} = - \dfrac{1}{25} + \dfrac{1}{45}} \\ \\ \rightarrow \: \sf{ \dfrac{1}{v} = \dfrac{- 9 + 5 }{225} }\\ \\ \rightarrow \: \sf{v = - \dfrac{225 }{4} } \\ \\ \rightarrow \: \bf{v = - 56.25 \: cm \: }$

As we know that when the object is placed on centre of curvature , the image also forms on the centre of curvature in the case of concave mirror

• Nature of the image is real and inverted
• Same size

Accordingly the image displaces –

⪼ 56.25 – 50

⪼ 6.25 cm

The displacement of the image is 6.25 cm behind the centre of curvature .