JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2021
- Hard
- MCQ
Curved surfaces of a plano-convex lens of refractive index \(\mu_{1}\) and a plano-concave lens of refractive index \(\mu_{2}\) have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.
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Answer & Solution
Correct Answer
(B) \(\mu_{1}-\mu_{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{{f}_{1}}=\left(\mu_{1}-1\right)\left(\frac{1}{{R}}\right)\)
\(\frac{1}{{f}_{2}}=\left(\mu_{2}-1\right)\left(-\frac{1}{{R}}\right)\)
\(\frac{1}{{f}_{1}}+\frac{1}{{f}_{2}}=\frac{1}{{f}_{{eq}}}=\frac{\left(\mu_{1}-1\right)-\left(\mu_{2}-1\right)}{{R}}\)
\(\frac{1}{f_{e q}}=\frac{\left(\mu_{1}-\mu_{2}\right)}{R}\)
\(\frac{{R}}{{f}_{{eq}}}=\left(\mu_{1}-\mu_{2}\right)\)
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