A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:
- -160 cm
- 160 cm
- 16 cm
- -16 cm
The Correct Option is A
Approach Solution - 1
To determine the focal length of a biconvex lens immersed in a liquid, we need to apply the lens maker's formula, which takes into account the change in refractive index of the surrounding medium.
The lens maker's formula is given by:
\[\frac{1}{f} = \left( \frac{n_{\text{lens}}}{n_{\text{medium}}} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]Let's break down the steps:
- Initially, the lens is in air. The refractive index of the lens, \(n_{\text{lens}}\), is 1.5 and that of air, \(n_{\text{medium}}\), is 1.0. Substituting these values into the lens formula when the lens is in air gives us the initial focal length, \(f_{\text{air}}\), of 20 cm. This is expressed as:
- Re-arranging this to solve for \(\frac{1}{R_1} - \frac{1}{R_2}\):
- Now, when the lens is immersed in a liquid with a refractive index, \(n_{\text{medium}} = 1.6\), we use the same lens maker's formula:
- Substitute \(\frac{1}{R_1} - \frac{1}{R_2} = \frac{1}{10 \text{ cm}}\):
- Simplify:
- Hence, invert to find the focal length:
Therefore, the focal length of the lens when immersed in a liquid of refractive index 1.6 is -160 cm.
Approach Solution -2
Step 1: Given Data: - Refractive index of the lens μl = 1.5 - Refractive index of the medium (liquid) μm = 1.6 - Focal length in air fa = 20 cm
Step 2: Use the Lens Formula in Different Mediums: - The relationship between the focal length in air fa and the focal length in the medium fm is given by:
\( \frac{f_m}{f_a} = \frac{\mu_l - 1}{\mu_l - \mu_m} \)
Step 3: Substitute the Values:
\( \frac{f_m}{20} = \frac{(1.5 - 1)}{(1.5 - 1.6)} \)
\( \frac{f_m}{20} = \frac{0.5}{-0.1} \)
\( f_m = 20 \times -5 = -160 \, \text{cm} \)
So, the correct answer is: -160 cm
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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.