61. An object is placed on the principal axis of a concave
mirror at a distance of 60 cm. If the focal length of
the concave mirror is 40 cm, then determine the
magnification of the obtained image.
Answers
Answer:
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Given: distance of object, u = 60cm
the focal length of the concave mirror, f = 40 cm
To Find: magnification of the obtained image, m.
Solution:
To calculate m , formula used:
- Magnification, m = - distance of image(v) / distance of object(u)
To calculate v, formula used:
- 1 / focal length = 1 / v + 1/ u ⇒ Mirror formula
here, f = - 40 cm
u = - 60 cm
Negative sign indicates that the mirror is concave.
Applying the formula for v:
- ( 1/40) = 1 / v + ( - 1/60)
1/ v = - ( 1/40) - (- 1/60)
= - 1/40 + 1/60
= -3 +2 / 120
= -1 / 120
Taking reciprocal on both the side:
v = - 120 cm
Applying thr formula for m:
m = - v / u
= - (-120) / - 60
= 120 / - 60
= - ( 12/6)
= - 2
m = -2
The negative sign indicates that the obtained image is inverted.
Hence, the magnification of the obtained image is -2.