Question

Two thin converging lens of powers diopters are placed coaxially apart

Answer 1

$Given,</p><p>Power of two lenses are P_{1}=+5DP1=+5D and P_{2}=+4DP2=+4D</p><p>We know that the The lens power is the inverse of the focal length in meters</p><p>therefore,</p><p>Focal length in meters (f)=\frac{1}{Power(P)}Focallengthinmeters(f)=Power(P)1</p><p>Focal length of lens 1 = f_{1}=\frac{1}{P_{1}}=\frac{1}{5}=0.2 m=20 cmf1=P11=51=0.2m=20cm</p><p>Focal length of lens 2 f_{2}=\frac{1}{P_{2}}=\frac{1}{4}=0.25 m=25 cmf2=P21=41=0.25m=25cm</p><p>The effective focal length (f) of a system of two lenses, separated by a distance d, is given by:</p><p>\begin{lgathered}f=\frac{f_{1}\times{f}_{2}}{f_{1}+f_{2}-d}\\\\\Rightarrow{f}=\frac{20\times25}{20+25+10}\\\\\Rightarrow{f}=\frac{500}{35\\\\\Rightarrow{f}=14.28\end{lgathered}f=f1+f2−df1×f2⇒f=20+25+1020×25⇒f=35500⇒f=14.28 cm</p><p>Hence, the effective focal length of the given system of lenses is +14.28 cm</p><p>$

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