SATHEE: Ray Optics and Optical Instruments

Ray Optics and Optical Instruments - Result Question 29

29. Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of $20 c m$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

[2015]

(a) $- 25 c m$

(b) $- 50 c m$

(d) $- 20 c m$

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Answer:

Correct Answer: 29. (b)

Solution:

(b) Using lens maker’s formula,

$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\Rightarrow \frac{1}{f_{1}} = (\frac{1.5}{1} - 1) (\frac{1}{\infty} - \frac{1}{- 20})$

$\Rightarrow f_{1} = 40 c m$

$\Rightarrow \frac{1}{f_{2}} = (\frac{1.7}{1} - 1) (\frac{1}{- 20} - \frac{1}{+ 20})$

$\Rightarrow f_{2} = - \frac{100}{7} c m$

Similarly,

$\Rightarrow \frac{1}{f_{3}} = (\frac{1.5}{1} - 1) (\frac{1}{\infty} - \frac{1}{- 20})$

$\Rightarrow f_{3} = 40 c m$

Now according to the condition

$\frac{1}{f_{e q}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$

$\Rightarrow \frac{1}{f_{eq}} = \frac{1}{40} + \frac{1}{- 100 / 7} + \frac{1}{40}$

$∴ f_{eq} = - 50 c m$

Therefore, the focal length of the combination is $- 50 c m$ .

For a system of lenses net focal length $F_{net}$

$= \frac{1}{f_{1}} + \frac{1}{f_{2}} + \dots + \frac{1}{f_{n}}$

Net power $P_{net} = P_{1} + P_{2} + \dots + P_{n}$

Ray Optics and Optical Instruments - Result Question 29

29. Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of $20 c m$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

Answer:

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Ray Optics and Optical Instruments - Result Question 29

29. Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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29. Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of $20 c m$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is