Optical Instruments

Astigmatism is an eye condition where the cornea or lens has an irregular shape, causing blurred or distorted vision. This defect arises due to an uneven curvature of the eye's lens or cornea, which does not focus light onto a single point of the retina.
The best way to correct astigmatism is by using a cylindrical lens, which has different curvatures in different directions. A cylindrical lens helps to focus light properly and corrects the uneven focus caused by the irregular shape of the cornea or lens.
- Convex lens (A): A convex lens is used to correct farsightedness (hyperopia), not astigmatism.
- Spherical lens (B): A spherical lens is used to correct myopia or hyperopia but is not ideal for astigmatism.
- Plano-convex lens (C): This lens has one flat surface and one convex surface, but it is not specifically designed for correcting astigmatism.
- Concave lens (D): A concave lens is used for myopia (nearsightedness), not for astigmatism.
Thus, the correct answer is (E) cylindrical lens.

Step 1: Use the lens maker's formula.
The lens maker's formula is given by: For a convex lens, (radius of curvature of the first surface) and (radius of curvature of the second surface). Substituting these values into the formula: Substitute : Therefore:
Final Answer: .

Step 1: Use the formula for the power of a lens.
The power of a lens is related to its focal length by the formula: where is the focal length in meters and is in diopters (D).
Step 2: Convert the focal length to meters.
The focal length of the first lens is given as 20 cm. Convert this to meters: The power of the first lens is:
Step 3: Calculate the total power of the combination.
The total power of the combination of two lenses in contact is the sum of the individual powers: where is the power of the second lens. Thus, the total power is: Therefore, the effective power of the combination is:

Concept:
• Magnifying power:

Step 1: Observation
Magnification inversely proportional to focal length.

Step 2: Conclusion
Smaller → higher magnification. Final Conclusion:
Option (B)