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A thin equi-convex lens of refractive index 3 / 2 is placed on a horizontal plane mirror as shown in the figure. The space between the lens and the mirror is then filled with water of refractive index 4 / 3 . It is found that when a point object is placed 15 cm above the lens on its principle axis, the object coincides with its own image. On repeating with another liquid, the object and the image again coincide at a

Correct answer

1.6

Step-by-step solution

RI of lens material = ₂ ; RI of first liquid = ₃ ; RI of air = ₁ ; RI of second liquid = ₃^ In general ( ₃ / v )- ( ₁ / u )= ( ₂- ₁ ) / R + ( ₃- ₂ ) / R Here u =-15 ~cm , v = Now, 1 /(+15)=[(3 / 2)-1 / R]-[ (4 / 3)-(3 / 2) / R] R=10 ~cm For the second liquid, similarly, (1 / 25)=(0.5 / R)- [ ^ ₃-(3 / 2) / R ] ^ ₃=1.6

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