KCET · Physics · Ray Optics
Two thin equiconvex lenses each of focal length \(0.2 \mathrm{~m}\) are placed coaxially with their optic centres \(0.5 \mathrm{~m}\) apart. Then the focal length of the combination is
- A \(-0.4 \mathrm{~m}\)
- B \(0.4 \mathrm{~m}\)
- C \(-0.1 \mathrm{~m}\)
- D \(0.1 \mathrm{~m}\)
Answer & Solution
Correct Answer
(A) \(-0.4 \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
Equivalent focal length \((F)\) of two lenses separated by distance \(\mathrm{d}\) is given by
\(\frac{1}{F} =\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{d}{f_{1} f_{2}} \)
\(=\frac{1}{0.2}+\frac{1}{0.2}-\frac{0.5}{(0.2)(0.2)} \)
\(=5+5-0.5 \times 5 \times 5 \)
\(=10-12.5=-2.5 \)
\(\therefore F =-\frac{1}{2.5}=-0.4 \mathrm{~m}\)
\(\frac{1}{F} =\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{d}{f_{1} f_{2}} \)
\(=\frac{1}{0.2}+\frac{1}{0.2}-\frac{0.5}{(0.2)(0.2)} \)
\(=5+5-0.5 \times 5 \times 5 \)
\(=10-12.5=-2.5 \)
\(\therefore F =-\frac{1}{2.5}=-0.4 \mathrm{~m}\)
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