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GUJCET · Physics · Ray Optics and Optical Instruments
What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 10 cm ? (Ignore thickness of lens)
- A -15 cm
- B -40 cm
- C -20 cm
- D -30 cm
Answer & Solution
Correct Answer
(A) -15 cm
Step-by-step Solution
Detailed explanation
(A) -15 cm
focal length of convex lens
\(
f_{1}=+30 \mathrm{~cm}
\)
focal length of concave lens
\(
f_{2}=-10 \mathrm{~cm}
\)
focal length of combination of lenses
\(
\begin{aligned}
& \quad \frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}} \\
& \therefore \quad \frac{1}{f}=\frac{1}{30}+\frac{1}{-10} \\
& \therefore \quad \frac{1}{f}=\frac{1-3}{30} \\
& \therefore \quad \frac{1}{f}=\frac{-2}{30} \\
& \therefore \quad f=-15 \mathrm{~cm}
\end{aligned}
\)
focal length of convex lens
\(
f_{1}=+30 \mathrm{~cm}
\)
focal length of concave lens
\(
f_{2}=-10 \mathrm{~cm}
\)
focal length of combination of lenses
\(
\begin{aligned}
& \quad \frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}} \\
& \therefore \quad \frac{1}{f}=\frac{1}{30}+\frac{1}{-10} \\
& \therefore \quad \frac{1}{f}=\frac{1-3}{30} \\
& \therefore \quad \frac{1}{f}=\frac{-2}{30} \\
& \therefore \quad f=-15 \mathrm{~cm}
\end{aligned}
\)
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