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Question
A 10 cm long stick is kept in front of a concave mirror having a focal length of 10 cm in such a way that the end of the stick closest to the pole is at a distance of 20 cm. What will be the length of the image?
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Solution
Given:
Length of stick = 10 cm
Distance of nearer end from mirror = 20 cm
So, distance of farther end = 20 + 10 = 30 cm
Focal length of concave mirror = 10 cm
Use the mirror formula:
`1/f = 1/v + 1/u`
Step 1: Image of the nearest end (u1 = 20 cm)
`1/10 = 1/v_1 + 1/20`
`1/v_1 =1/10 - 1/20 = 1/20`
v1 = 20 cm
Step 2: Image of the farthest end (u2 = 30 cm)
`1/10 = 1/v_2 + 1/30`
`1/v_2 = 1/10 - 1/30 = 2/30 = 1/15`
v2 = 15 cm
Step 3: Length of the image
The two image points form at 15 cm and 20 cm from the mirror.
Image length = ∣20 − 15∣ = 5 cm
The length of the image is 5 cm.
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Match the following:
| Column I | Column II | ||
| 1. | A plane mirror | a. | The image is erect & smaller in size than the object. |
| 2. | A concave mirror | b. | The image is erect & of the same size as the object. |
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| d. | Can form images of objects spread over a large area. |
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| Column I | Column II | ||
| 1. | plane mirror | a. | Focal length is positive. |
| 2. | concave | b. | The focal length is negative. |
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