Two thin convex lenses of focal length 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this…

Two thin convex lenses of focal length 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is :
  1. 5 D
  2. 1 D
  3. 20 D
  4. 10 D

Solution

$\mathrm{f}_1=30 \mathrm{~cm}, \mathrm{f}_2=10 \mathrm{~cm}$
$\frac{1}{\mathrm{f}_{\mathrm{eq}}}=\frac{1}{\mathrm{f}_1}+\frac{1}{\mathrm{f}_2}-\frac{\mathrm{d}}{\mathrm{f}_1 \mathrm{f}_2}, \mathrm{~d}=$ distance between lens
$\frac{1}{\mathrm{f}_{\mathrm{eq}}}=\frac{1}{0.3}+\frac{1}{0.1}-\frac{0.1}{(0.3)(0.1)}$
$\frac{1}{\mathrm{f}_{\mathrm{eq}}}=\frac{1}{0.1}$
Power $=\frac{1}{\mathrm{f}_{\mathrm{eq}}}=10 \mathrm{D}$

Asked in: JEE Main 2025 (07 Apr Shift 1)

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