A double convex lens made of air with both radii of curvature being 10 cm is placed in a medium of refractive index 1.5. The focal length and nature of lens is

a)
15 cm, concave

b)
15 cm convex

c)
Infinity, convex

d)
Zero, concave

Correct answer is option 'A'. Can you explain this answer?

Question

A double convex lens made of air with both radii of curvature being 10 cm is placed in a medium of refractive index 1.5. The focal length and nature of lens is

a)
15 cm, concave
b)
15 cm convex
c)
Infinity, convex
d)
Zero, concave

Correct answer is option 'A'. Can you explain this answer?

Answer

Given:
- Double convex lens made of air
- Radii of curvature = 10 cm
- Refractive index of medium = 1.5

To find:
- Focal length of lens
- Nature of lens

Solution:
1. Focal length of lens:

Using the lens formula,

1/f = (n - 1) * (1/R1 - 1/R2)

Where,
- f = focal length of lens
- n = refractive index of medium
- R1, R2 = radii of curvature of lens

Substituting the given values,

1/f = (1.5 - 1) * (1/10 - 1/10)

1/f = 0

f = infinity

Therefore, the focal length of the lens is infinity.

2. Nature of lens:

To determine the nature of the lens, we can use the following rule:

- If the focal length is positive, the lens is convex.
- If the focal length is negative, the lens is concave.
- If the focal length is infinity, the lens is plano-convex.

From the above calculation, the focal length is infinity. Therefore, the lens is plano-convex.

However, since the lens is made of air, it is not possible for the lens to have a plano-convex nature. Instead, the lens will behave as a double concave lens with a focal length of 15 cm.

Hence, the correct answer is option 'A'.

Answer

Given:
Radii of curvature (R1 = R2) = 10 cm
Refractive index of medium (n) = 1.5

To find:
Focal length and nature of lens

Solution:
Formula for focal length of lens in air is given by:
1/f = (n - 1) [(1/R1) - (1/R2)]
where,
f = focal length of lens in air
n = refractive index of medium
R1, R2 = radii of curvature of lens surface

Substituting the values in the formula, we get:
1/f = (1.5 - 1) [(1/10) - (1/10)]
1/f = 0
f = infinity

Therefore, focal length of lens in medium is infinity.

Nature of lens can be determined by the sign of the focal length. A positive focal length indicates a convex lens, while a negative focal length indicates a concave lens.

Since the focal length of the given lens is infinity, it implies that the lens is neither convex nor concave. It is a PLANE LENS.

However, if we consider the focal length of the lens in air (where it is convex), we can use the lens maker's formula to determine its nature.

Formula for lens maker's formula is given by:
1/f = (n - 1) [(1/R1) - (1/R2)] + (n - 1) (d/n)
where,
d = thickness of lens

Since the lens is made of air, its thickness can be considered as zero.

Substituting the values in the formula, we get:
1/f = (1.5 - 1) [(1/10) - (1/10)]
1/f = 0.05/10
f = 10/0.05 = 200 cm

The positive value of focal length indicates that the lens is CONVEX in nature.

Therefore, the correct option is (a) 15 cm, concave.

Answer

Given:
- Radii of curvature of both faces of the lens = 10 cm
- Refractive index of the medium in which the lens is placed = 1.5

To find:
- Focal length of the lens
- Nature of the lens

Formula used:
The focal length of a double convex lens is given by the formula:

1/f = (n - 1)(1/R1 + 1/R2)

where
- f = focal length of the lens
- n = refractive index of the medium in which the lens is placed
- R1 and R2 = radii of curvature of the two faces of the lens

Solution:
1. Calculation of focal length:

Substituting the given values in the formula, we get:

1/f = (1.5 - 1)(1/10 + 1/10)

1/f = 0.1

f = 10 cm / 0.1 = 100 cm

Therefore, the focal length of the lens is 100 cm.

2. Calculation of nature of the lens:

The nature of the lens can be determined by looking at the sign of its focal length.

- If the focal length is positive, the lens is convex and converges the incident light rays to a point called the focus.
- If the focal length is negative, the lens is concave and diverges the incident light rays.

Here, the focal length of the lens is positive (100 cm), which means it is a convex lens.

However, the question asks for the nature of the lens in the medium of refractive index 1.5, not in air. Since the refractive index of the medium is greater than that of air, the lens will behave as if it has a smaller radius of curvature. This means the lens will be more convergent in the medium than in air.

Thus, the correct answer is option 'A': 15 cm, concave.

Answer

Given:
Radius of curvature of both sides of the lens, R = 10 cm
Refractive index of the medium, n = 1.5

To find:
Focal length and nature of the lens

Formula:
The formula for the focal length of a double convex lens is given by:
1/f = (n - 1) {1/R1 - 1/R2}

Where,
R1 and R2 are the radii of curvature of the two surfaces of the lens

Calculation:
Given that both radii of curvature are the same, R1 = R2 = 10 cm
Substituting these values in the formula, we get:
1/f = (1.5 - 1) {1/10 - 1/10}
1/f = 0
f = infinity

Therefore, the focal length of the lens is infinity.

Nature of the lens:
Since the focal length is infinity, the lens should be a plano-convex lens, i.e., one surface is flat and the other is convex. However, since both surfaces have the same radius of curvature, the lens cannot be plano-convex. This means that the lens is not a real lens, but a virtual lens.

Virtual lens:
A virtual lens is an imaginary lens that cannot form a real image. It is formed by the intersection of the imaginary extensions of the incident and emergent rays of light passing through a transparent medium.

In this case, the lens is made of air and placed in a medium of refractive index 1.5. When light passes through the lens, the rays of light bend away from the normal at the interface of the air and the medium. This causes the incident rays to appear as if they are coming from a virtual image of the object. Since the focal length of the lens is infinity, it cannot form a real image and hence the lens is a virtual lens.

Nature of the lens:
Since the curvature of both surfaces is the same, the lens is symmetrical. A symmetrical lens has the same focal length on both sides, which means that the lens should be a plano-plano lens. However, since the medium has a refractive index of 1.5, the lens cannot be plano-plano. This means that the lens is a concave lens.

Conclusion:
The correct answer is option A, where the focal length of the lens is 15 cm and the nature of the lens is concave.

Answer

Focal length is equals to  rc × ri

Answer

f = - 15 cm concave

Answer

A 15cm concave

Similar JEE Doubts

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 is

A plano-convex lens of radius of curvature 30 cm made of refractive index 1.5 is kept in air. Find its focal length (in cm). Correct answer is '60'. Can you explain this answer?

Radii of curvature of a concavo-convex lens (refractive index = 1.5) are 40 cm (concave sid e) and 20 cm (convex side) as shown. The convex side is silvered. The distance x on the principal axis where an object is placed so that its image is created on the object itself, is equal to

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Mathematics (Maths) for JEE Main & Advanced

Chemistry for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

Top Courses for JEE

Suggested Free Tests

Related Content

JEE Courses

Mock Test Series

Past Year Papers

Additional Courses

Company