Ray Optics

JEE Main level, numerical answer, medium

218 of 295

Question 218 of 295

Two convex lenses of focal length 20cm20cm each are placed coaxially with a separation of 60cm60cm between them. The image of the distant object formed by the combination is at _____ cmcm from the first lens.

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Answer: 100

Let L1{L}_{1} be the first lens and L2{L}_{2} be the second lens.
The first refraction is in L1{L}_{1}.
Using lens formula,
u1=∞,f1=20cm,1v1−0=1f1⇒v1=20cm{u}_{1}=\infty ,{f}_{1}=20cm, \dfrac{1}{{v}_{1}}-0=\dfrac{1}{{f}_{1}} \Rightarrow {v}_{1}=20cm
Hence, the distance between the second image and the L2{L}_{2} would be (60−20)=40cm\left(60-20\right)=40cm.
For the second lens L2{L}_{2},
u2=−40cm,f2=20cm,1v2−1u2=1f2⇒1v2+140=120⇒1v2=140⇒v2=40cm{u}_{2}=-40cm,{f}_{2}=20cm, \dfrac{1}{{v}_{2}}-\dfrac{1}{{u}_{2}}=\dfrac{1}{{f}_{2}} \Rightarrow \dfrac{1}{{v}_{2}}+\dfrac{1}{40}=\dfrac{1}{20} \Rightarrow \dfrac{1}{{v}_{2}}=\dfrac{1}{40} \Rightarrow {v}_{2}=40cm
So, the distance of image from first lens is
x=40cm+60cmx=40cm+60cm
=100cm=100cm

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