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?

Question

Answer

R₁ = ∝
R₂ = –30 cm

f = 60 cm

Answer

R₁ = ∝
R₂ = –30 cm

f = 60 cm

Answer

Given:
- Radius of curvature (R) = 30 cm
- Refractive index of lens (n) = 1.5
- Medium surrounding the lens = Air

To find:
- Focal length of the lens

Formula:
The formula to calculate the focal length of a plano-convex lens is:

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

Where:
- f is the focal length of the lens
- R1 is the radius of curvature of the curved surface of the lens
- R2 is the radius of curvature of the flat surface of the lens

Solution:

- Given that the lens is plano-convex, one of its surfaces is flat and the other is curved. Therefore, the radius of curvature of the flat surface is infinity.

- Substituting the given values into the formula, we have:

1/f = (1.5 - 1) * (1/R - 1/infinity)

Since 1/infinity is equal to zero, the term becomes:

1/f = 0 - (1/R)

Simplifying further:

1/f = -1/R

- Multiply both sides by f:

f * (1/f) = f * (-1/R)

1 = -f/R

- Rearranging the equation, we get:

f = -R

- Substituting the value of R, we have:

f = -30 cm

- The negative sign indicates that the focal length is on the opposite side of the lens from the curved surface, which is the side facing the air.

- Therefore, the focal length of the lens is 30 cm.

Conclusion:
The focal length of the plano-convex lens with a radius of curvature of 30 cm and a refractive index of 1.5 is 30 cm.

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