Size of an image of an object by a mirror having a focal length 20 cm is observed to be reduced 1/3 of its size. At what distance the object has been placed from the mirror? What is the nature of the image and that of the mirror?
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Answered by
6
In case of concave mirror
f=-20cm
As specific denotion
h2=1/3 h1
h2/h1=1/3=m
m=-v/u=1/3
v=-1/3u
applying mirror formula
1/f=1/v+1/u
1/-20=-3u/1+1/u
-1/20=-3u²+1
-u=-60u²+20
60u²-u-20=0
solve this equation by using quadratic equation, the answer will be
u=71/120
u=69/120
f=-20cm
As specific denotion
h2=1/3 h1
h2/h1=1/3=m
m=-v/u=1/3
v=-1/3u
applying mirror formula
1/f=1/v+1/u
1/-20=-3u/1+1/u
-1/20=-3u²+1
-u=-60u²+20
60u²-u-20=0
solve this equation by using quadratic equation, the answer will be
u=71/120
u=69/120
Answered by
0
Answer.
Here, it is not given whether the lens is concave of convex. So, we will do calculations for both types of mirror.
For concave mirror:
Focal length, f = ‒ 20 cm
Magnification, m = −1/3
Since, magnification, m = − v/u
Magnification, m = −1/3 = − v/u
⟹ v = u/3
Hence, object must be placed at a distance 40 cm from the pole of convex mirror to form erect , virtual, and diminished image.
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