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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Geometrical Optics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Geometrical Optics

Consider a double convex lens that has two surfaces of equal radii...

Consider a double convex lens that has two surfaces of equal radii RR and a refractive index m=1.5m = 1.5. The focal length ff is given by:

Options

  1. Af=−Rf = -R
  2. Bf=R/2f = R/2
  3. Cf=Rf = R
  4. Df=2Rf = 2R

Correct answer

C. f=Rf = R

Step-by-step solution

Using the lens maker's formula:

\dfrac{1}{f} = (m - 1) \left(\dfrac{1}{R_1} - \dfrac{1}{R_2} \right)

For a double convex lens, the radii of curvature are R1=RR_1 = R and R2=−RR_2 = -R.

Given m=1.5m = 1.5:

\dfrac{1}{f} = (1.5−1)(1R−1−R)1.5 - 1) \left( \dfrac{1}{R} - \dfrac{1}{-R} \right)

\dfrac{1}{f} = 0.5 \left(\dfrac{2}{R} \right)

\dfrac{1}{f} = \dfrac{1}{R}

f=Rf = R
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