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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

The radii of curvature of a lens are +20 cm and +30 cm . The...

The radii of curvature of a lens are +20 cm+20 \text{ cm} and +30 cm+30 \text{ cm}. The refracting index of the lens material is 1.61.6. Find the focal length of the lens if it is placed in water (μ=1.33\mu = 1.33).

Options

  1. A−300 cm-300 \text{ cm}
  2. B400 cm400 \text{ cm}
  3. C300 cm300 \text{ cm}
  4. D100 cm100 \text{ cm}

Correct answer

C. 300 cm300 \text{ cm}

Step-by-step solution

Using the lens maker's formula:

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

Given μl=1.6\mu_l = 1.6, μm=1.33≈\mu_m = 1.33 \approx\dfrac{4}{3}, R1=+20 cmR_1 = +20 \text{ cm}, and R2=+30 cmR_2 = +30 \text{ cm}.

Substituting the values:

\dfrac{1}{f} = \left( \dfrac{1.6}{4/3} - 1 \right) \left( \dfrac{1}{20} - \dfrac{1}{30} \right)<br><br><br><br>\dfrac{1}{f} = \left( 4.84−\dfrac{4.8}{4} -1 \right) \left( \dfrac{3 - 2}{60} \right)<br><br>\dfrac{1}{f} = (1.2 - 1) \times 160<br><br>1f=\dfrac{1}{60}<br><br>\dfrac{1}{f} =0.2 \times 160=15×160<br><br>1f=1300<br><br>\dfrac{1}{60} = \dfrac{1}{5} \times \dfrac{1}{60}<br><br>\dfrac{1}{f} = \dfrac{1}{300}<br><br>f = 300 \text{ cm}
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