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Question:

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object?

65.0 cm

124.5 cm

144.5 cm

99.0 cm

Solution:

1st position
u=-x, v=+y
m1=v/u=+y/-x
2nd position
u=-y, v=+x
m2=v/u=+x/-y
Also, m1/m2=3/2 (given)
y/-x / x/-y = 3/2
y/x * y/x = 3/2
y²/x² = 3/2
y = √(3/2)x
y - x = 10
By Solving these above equations, we get
y=44.5, x=54.5
So, d=x+y=99cm