Question:
A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is of the ratio of their focal length is $\frac{3}{2}$ Their equivalent focal length is 30 cm. What are their individual focal lengths ?
A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is of the ratio of their focal length is $\frac{3}{2}$ Their equivalent focal length is 30 cm. What are their individual focal lengths ?
Updated On: Jan 18, 2023
- -75, 50
- -10, 15
- 75, 50
- -15, 10
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The Correct Option is D
Solution and Explanation
Let focal length of convex lens is + f then focal length of
concave lens would be $-\frac{3}{2} f.$
From the given condition.
$\frac{1}{30}=\frac{1}{f}-\frac{2}{3 f}=\frac{1}{3 f}$
$\therefore \hspace15mm f=10 cm$
Therefore, focal length of convex lens = + 10 cm
and that of concave lens =- 15 cm
$\therefore$ Correct answer is (d).
concave lens would be $-\frac{3}{2} f.$
From the given condition.
$\frac{1}{30}=\frac{1}{f}-\frac{2}{3 f}=\frac{1}{3 f}$
$\therefore \hspace15mm f=10 cm$
Therefore, focal length of convex lens = + 10 cm
and that of concave lens =- 15 cm
$\therefore$ Correct answer is (d).
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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.