Question:
The power of biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is
The power of biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is
Updated On: Jun 7, 2022
- $\frac{3}{2}$
- $\frac{4}{3}$
- $\frac{9}{8}$
- $\frac{5}{3}$
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The Correct Option is A
Solution and Explanation
Power of lens,
$P { (in\, dioptre)= \frac{100}{focal \, length \, f (in \, cm)}}$
$\therefore \:\:\:\: f = \frac{100}{10} = { 10 \, cm}$
According to lens maker?s formula
$\frac{1}{f} = (\mu -1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$
For biconvex lens, $R_1 = + R, R_2 = - R$
$ \therefore \:\: \frac{1}{f}=\left(\mu-1\right)\left(\frac{1}{R} - \frac{1}{R}\right) $
$\frac{1}{f}=\left(\mu-1\right)\left(\frac{2}{R}\right)$
$\frac{1}{10}=\left(\mu-1\right)\left(\frac{2}{10}\right)$
$ \left(\mu-1\right)=\frac{1}{2} \Rightarrow \mu=\frac{1}{2}+1=\frac{3}{2}$
$P { (in\, dioptre)= \frac{100}{focal \, length \, f (in \, cm)}}$
$\therefore \:\:\:\: f = \frac{100}{10} = { 10 \, cm}$
According to lens maker?s formula
$\frac{1}{f} = (\mu -1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$
For biconvex lens, $R_1 = + R, R_2 = - R$
$ \therefore \:\: \frac{1}{f}=\left(\mu-1\right)\left(\frac{1}{R} - \frac{1}{R}\right) $
$\frac{1}{f}=\left(\mu-1\right)\left(\frac{2}{R}\right)$
$\frac{1}{10}=\left(\mu-1\right)\left(\frac{2}{10}\right)$
$ \left(\mu-1\right)=\frac{1}{2} \Rightarrow \mu=\frac{1}{2}+1=\frac{3}{2}$
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Concepts Used:
Spherical Lenses
Lenses that are made by combining two spherical transparent surfaces are called spherical lenses. In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.
Properties of Convex lens:
- In this, the lenses are thicker in the middle and thinner at the edges.
- They have a positive focal length.
- It intersects the incident rays towards the principal axis
- These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.
Properties of Concave lens:
- These lenses are thinner in the middle and thicker at the edges.
- They have a negative focal length.
- It parts the incident rays away from the principal axis.
- These are used in the glasses, spy holes, some telescopes in the doors, etc.