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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Dispersion and Spectra

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Dispersion and Spectra

Considering only the magnitudes, which of the following quantities...

Considering only the magnitudes, which of the following quantities increase as the wavelength is increased?

Options

  1. AThe focal length of a diverging lens.
  2. BThe power of a converging lens.
  3. CThe power of a diverging lens.
  4. DThe focal length of a converging lens.

Correct answer

D. The focal length of a converging lens.

Step-by-step solution

According to Cauchy's formula, the refractive index of a material is given by μ=A+Bλ2\mu = A + \dfrac{B}{\lambda^2}.

As the wavelength λ\lambda increases, the refractive index μ\mu decreases.

From the lens maker's formula, the focal length ff is given by 1f=(μ−1)\dfrac{1}{f} = (\mu - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right).

The power of a lens is defined as P=P =\dfrac{1}{f}.

Since μ\mu decreases with an increase in λ\lambda, the term (μ−1)(\mu - 1) decreases. This implies that the magnitude of \dfrac{1}{f} decreases, and consequently, the magnitude of the focal length ff increases.

Therefore, the magnitude of the focal length of both a converging lens and a diverging lens increases as the wavelength is increased. The magnitude of the power of both lenses decreases.
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