Two plano convex lenses of focal lengths $f_{1}$ and $f_{2}$ set for minimising spherical aberration are kept apart by 2 cm. If the equivalent focal length of combination is 10 cm, the values of $f_{1}$ and $f_{2}$ are :

Question

Two plano convex lenses of focal lengthsf1 andf2 minimising spherical aberration are kept apart by 2 cm- If the equivalent focal length of combination is 10 cm- the values of f1 and f2 are -

Toppr Admin · Accepted Answer

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Two plano convex lenses of focal lengthsf1 andf2 set for minimising spherical aberration are kept apart by 2 cm. If the equivalent focal length of combination is 10 cm, the values of f1 and f2 are :

d=f2−f1⇒f2−f1=2 ⇒f2=2+f1feq=f1f2f1+f2−d=f1f2f1+f2−2=10(f1)(2×f1)(2f1)=102+f1=20f1=18cmf2=2+f1=20cm

Two plano convex lenses of focal lengths $f_{1}$ and $f_{2}$ set for minimising spherical aberration are kept apart by 2 cm. If the equivalent focal length of combination is 10 cm, the values of $f_{1}$ and $f_{2}$ are :

$d = f_{2} - f_{1}$

$\Rightarrow f_{2} - f_{1} = 2$ $\Rightarrow f_{2} = 2 + f_{1}$

$f_{e q} = \frac{f_{1} f_{2}}{f_{1} + f_{2} - d} = \frac{f_{1} f_{2}}{f_{1} + f_{2} - 2} = 10$

$\frac{(f_{1}) (2 \times f_{1})}{(2 f_{1})} = 10$

$2 + f_{1} = 20$

$f_{1} = 18 c m$

$f_{2} = 2 + f_{1} = 20 c m$