A 2.0cm high object is placed at a distance of 20cm from a spherical mirror which forms a real image at 40cm from the mirror. Calculate the focal length of the mirror and size of the image. Is the mirror converging or diverging.
Answers
Answer:
Focal Length = - 13.33 cm
Size of the image = h2 = - 4cm
Explanation:
Given Data -
u = - 20 cm
h1 (Height of the object) = 2 cm
v = - 40 cm
To find -
Focal Length, Size of the image (h2) and whether it is Converging mirror or Diverging mirror.
Calculation -
As it is given that the image forms a Real image thus it means, that the image is Real and Inverted. Hence, the v will be negative
From the above observations, we can conclude that it is a Concave mirror and thus a Converging Mirror.
Formula
1/v + 1/u = 1/f
1/ -40 + 1/ - 20 = 1/f
(-1/40 )+ (-1/20) = 1/f
Taking LCM of 40 and 20 = 40
(-1) + (-2)/40 = 1/f
-3/40 = 1/f
Thus,
f = -40/3
f = -13.33 cm
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Now,
Calculating the Size of the image
-v/u = h2/h1
- (-40) /-20 = h2/2
80 = -20h2
Thus,
h2 = -80/20
h2 = -4 cm
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