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AIIMS 201926 May
Exam
AIIMS
Year
2019
Date
26 May
Subject
Physics
Chapter
Ray Optics

AIIMS 2019 · 26 May · Physics · Ray Optics

A bi-convex lens is formed with two thin plano-convex lenses as...

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index nn of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R=14 cmR=14 \mathrm{~cm}. For this bi-convex lens, for an object distance of 40 cm40 \mathrm{~cm}, the image distance will be A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first

Options

  1. A−280.0 cm-280.0 \mathrm{~cm}
  2. B40.0 cm40.0 \mathrm{~cm}
  3. C21.5 cm21.5 \mathrm{~cm}
  4. D13.3 cm13.3 \mathrm{~cm}

Correct answer

B. 40.0 cm40.0 \mathrm{~cm}

Step-by-step solution

According to lens maker's formula 1f=(n−1)\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)Forthefirstlens:For the first lens :n=1.5, R_1=+14 \mathrm{~cm}, R_2=\infty \therefore \quad \frac{1}{f_1}=(1.5-1)(114−1∞)=0.514\left(\frac{1}{14}-\frac{1}{\infty}\right)=\frac{0.5}{14} For the second lens : n=1.2,R1=∞,R2=−14 cmn=1.2, R_1=\infty, R_2=-14 \mathrm{~cm} ∴1f2=(1.2−1)\therefore \quad \frac{1}{f_2}=(1.2-1)\left(\frac{1}{\infty}-\frac{1}{-14}\right)=\frac{0.2}{14}Thefocallengthofthebi−convexlensisThe focal length of the bi-convex lens is\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{0.5}{14}+\frac{0.2}{14}=\frac{0.7}{14}=\frac{1}{20}Accordingtothinlensformula;According to thin lens formula;\frac{1}{v}-\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{v}-\frac{1}{-40}=\frac{1}{20}ororv=40 \mathrm{~cm}
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