As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance x= _________ cm, from concave lens.

Solution

Physics sir · 4 steps

Take it one lens at a time: the concave lens's image becomes the object for the convex lens.

1. Focal lengths. Each lens has one flat face (R = ∞) and one curved face with |R| = 30 cm. The lens maker's formula gives 1/|f| = (1.75 - 1)1/30 = 1/40. So the concave lens has f₁ = -40 cm and the convex lens has f₂ = +40 cm.
2. First lens. Parallel rays from infinity leave the concave lens diverging, as if they came from its focus. That virtual image I₁ sits 40 cm to the left of the concave lens.
3. Object for convex. The convex lens is 40 cm to the right of the concave lens. So I₁ is 40 + 40 = 80 cm to the left of the convex lens, which gives u = -80 cm.

   1/v = 1/f₂ + 1/u = 1/40 - 1/80 = 1/80 ⇒ v = +80 cm

4. So. The final image is 80 cm to the right of the convex lens. Measured from the concave lens, x = 40 + 80 = 120 cm.

The common slip: 80. Stopping at the convex lens's image distance gives 80, but x is measured from the concave lens, so add the 40 cm gap.

The idea to keep. When two lenses are separated, do not add powers. Find the image from the first lens, shift it to the second lens's position, and use it as the new object.

Answer from the NTA final answer key. Solution by PrepWiser.