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प्रश्न
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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उत्तर
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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संबंधित प्रश्न
Write the spherical mirror formula and explain the meaning of each symbol used in it.
The mirror formula is ______.
Assertion: The mirrors used in torch lights are parabolic, not concave.
Reason: The image formed by a concave mirror is always virtual.
Assertion: The nature of the image depends on the size of the mirror.
Reason: Small mirrors always form a virtual image.
Which kind of mirrors are used in the shaving mirror? Why?
Which mirror is used as a reflector? Why?
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. |
| 3. | A convex | c. | Used by dentists to see an enlarged image of teeth. |
| d. | Can form images of objects spread over a large area. |
Match the following:
| Column I | Column II | ||
| 1. | plane mirror | a. | Focal length is positive. |
| 2. | concave | b. | The focal length is negative. |
| 3. | convex | c. | The focal length is infinity. |
| 4. | Real image | d. | Magnification if positive value. |
| 5. | Virtual image | e. | Magnification if negative value. |
