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Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surface towards each other and the space between them is filled with liquid of refractive index 4/3. Then the combination is
- a)convex lens of focal length 70 cm
- b)concave lens of focal length 70 cm
- c)concave lens of focal length 66.6 cm
- d)convex lens of focal length 66.6 cm
Correct answer is option 'C'. Can you explain this answer?
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Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 ha...
Given data:
- Refractive index of glass lens, ng = 1.5
- Radii of curvature of lens 1, R1 = -25 cm (negative sign indicates concave surface)
- Radii of curvature of lens 2, R2 = -20 cm (negative sign indicates concave surface)
- Refractive index of liquid, nl = 4/3
To find: The combined lens is a concave lens of focal length.
Solution:
When two thin lenses are in contact with each other, the effective focal length of the combination can be calculated using the lens formula:
1/f = (ng - nl) * (1/R1 - 1/R2)
- Since the lenses are in contact, their separation is zero, and the space between them is filled with liquid. Therefore, the effective refractive index between the lenses will be that of the liquid, i.e., nl.
- When light travels from a medium with a higher refractive index to a medium with a lower refractive index (ng > nl), the lens behaves as a diverging lens or a concave lens.
Using the lens formula, we can calculate the effective focal length of the combination:
1/f = (1.5 - 4/3) * (1/-25 - 1/-20)
Simplifying the equation:
1/f = (-1/6) * (4/500 - 5/500)
1/f = (-1/6) * (-1/500)
1/f = 1/3000
f = 3000 cm
The focal length of the combination is 3000 cm or 30 m.
Since the combination behaves as a concave lens, the negative sign indicates that the focal length is negative, i.e., the combination is a concave lens of focal length -30 m or -3000 cm.
Therefore, the correct option is (c) concave lens of focal length 66.6 cm.
- Refractive index of glass lens, ng = 1.5
- Radii of curvature of lens 1, R1 = -25 cm (negative sign indicates concave surface)
- Radii of curvature of lens 2, R2 = -20 cm (negative sign indicates concave surface)
- Refractive index of liquid, nl = 4/3
To find: The combined lens is a concave lens of focal length.
Solution:
When two thin lenses are in contact with each other, the effective focal length of the combination can be calculated using the lens formula:
1/f = (ng - nl) * (1/R1 - 1/R2)
- Since the lenses are in contact, their separation is zero, and the space between them is filled with liquid. Therefore, the effective refractive index between the lenses will be that of the liquid, i.e., nl.
- When light travels from a medium with a higher refractive index to a medium with a lower refractive index (ng > nl), the lens behaves as a diverging lens or a concave lens.
Using the lens formula, we can calculate the effective focal length of the combination:
1/f = (1.5 - 4/3) * (1/-25 - 1/-20)
Simplifying the equation:
1/f = (-1/6) * (4/500 - 5/500)
1/f = (-1/6) * (-1/500)
1/f = 1/3000
f = 3000 cm
The focal length of the combination is 3000 cm or 30 m.
Since the combination behaves as a concave lens, the negative sign indicates that the focal length is negative, i.e., the combination is a concave lens of focal length -30 m or -3000 cm.
Therefore, the correct option is (c) concave lens of focal length 66.6 cm.
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Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contactwith their curved surface towards each other and the space between them is filled with liquid of refractive index 4/3. Then the combination isa)convex lens of focal length 70 cmb)concave lens of focal length 70 cmc)concave lens of focal length 66.6 cmd)convex lens of focal length 66.6 cmCorrect answer is option 'C'. Can you explain this answer?
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Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contactwith their curved surface towards each other and the space between them is filled with liquid of refractive index 4/3. Then the combination isa)convex lens of focal length 70 cmb)concave lens of focal length 70 cmc)concave lens of focal length 66.6 cmd)convex lens of focal length 66.6 cmCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contactwith their curved surface towards each other and the space between them is filled with liquid of refractive index 4/3. Then the combination isa)convex lens of focal length 70 cmb)concave lens of focal length 70 cmc)concave lens of focal length 66.6 cmd)convex lens of focal length 66.6 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contactwith their curved surface towards each other and the space between them is filled with liquid of refractive index 4/3. Then the combination isa)convex lens of focal length 70 cmb)concave lens of focal length 70 cmc)concave lens of focal length 66.6 cmd)convex lens of focal length 66.6 cmCorrect answer is option 'C'. Can you explain this answer?.
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Solutions for Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contactwith their curved surface towards each other and the space between them is filled with liquid of refractive index 4/3. Then the combination isa)convex lens of focal length 70 cmb)concave lens of focal length 70 cmc)concave lens of focal length 66.6 cmd)convex lens of focal length 66.6 cmCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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