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प्रश्न
The image formed by a spherical mirror is real, inverted and is of magnification -2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.
उत्तर
Given: Magnification, m = -2
Distance of the image, v = -30 cm
Magnification, `m=-v/u`
∴`u=-v/m=-((-30))/((-2))`
∴u = -15 cm
Substituting these values in the mirror formula
`1/f=1/v+1/u`
=`1/((-30))+1/((-15))`
`1/f=-1/10`
∴f = 10 cm
When the object is moved 10 cm towards the mirror the new position of the object is
u' = -(15-10) = 5 cm
Substituting the new value in the mirror formula
`1/f=1/v+1/u`
`1/v^'=1/f-1/u=1/10-1/((-5))`
`1/v^'=1/10`
∴v' = 10 cm
Thus, the image is located 10 cm behind the mirror.
And magnification,`m'=(v')/(u')=-10/((-5))`
m' = 2
Since magnification is positive the image is erect and virtual.
Thus, the image is erect,virtual and magnified in nature.
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संबंधित प्रश्न
A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50 cm from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from the object.
(c) What is the focal length of the mirror?
(d) Draw the ray diagram to show the image formation in this case.
A student was asked by his teacher to find the image distance for various object distance in case of a given convex lens. He performed the experiment with all precautions and noted down his observations in the following table:
| S. No. |
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Image distance (cm) |
| 1 | 60 | 15 |
| 2 | 48 | 16 |
| 3 | 36 | 21 |
| 4 | 24 | 24 |
| 5 | 18 | 36 |
| 6 | 16 | 48 |
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(A) 2
(B) 3
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