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.
Answer: 120
Solution
Each lens has ∣f∣1=(μ−1)R1=300.75, so the plano-concave lens has focal length f1=−40 cm and the plano-convex lens f2=+40 cm. Parallel light from infinity leaves the concave lens as though diverging from a virtual image at its focus, 40 cm in front of it, which lies 40+40=80 cm ahead of the convex lens. Applying v1=f21+u1 with u=−80 cm gives v=80 cm beyond the convex lens. Measured from the concave lens, the image forms at 40+80=120 cm.
JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Integer answer
