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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

A lens has radii of curvature of +20 cm and +30 cm . The material...

A lens has radii of curvature of +20 cm+20 \text{ cm} and +30 cm+30 \text{ cm}. The material of the lens has a refracting index of 1.61.6. Determine the focal length of the lens when it is placed in air.

Options

  1. A−20 cm-20 \text{ cm}
  2. B−100 cm-100 \text{ cm}
  3. C20 cm20 \text{ cm}
  4. D100 cm100 \text{ cm}

Correct answer

D. 100 cm100 \text{ cm}

Step-by-step solution

Using the Lens Maker's formula:

1f=(μ−1)\dfrac{1}{f} = (\mu - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)

Given R1=+20 cmR_1 = +20 \text{ cm}, R2=+30 cmR_2 = +30 \text{ cm}, and μ=1.6\mu = 1.6.

Substituting the values:

\dfrac{1}{f} = (1.6−1)(120−130)1.6 - 1) \left(\dfrac{1}{20} - \dfrac{1}{30}\right)

1f=0.6×\dfrac{1}{f} = 0.6 \times\left(\dfrac{3 - 2}{60}\right)

\dfrac{1}{f} =0.6×0.6 \times\dfrac{1}{60}

\dfrac{1}{f} = \dfrac{1}{100}

f=+100 cmf = +100 \text{ cm}
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