Power of a Lens - UNSOLVED PRACTICE SET

Q7. Define the power of a lens. Write its SI unit and dimensional formula.

Q8. A lens has a power of −5 D. Is it convex or concave? Calculate its focal length.

Q9. Why is the power of a convex lens positive and that of a concave lens negative?

Q10. An optician prescribes glasses of power +2.5 D for a person. What type of lens is this and what is its focal length?

Q11. How does the power of a lens change when it is placed in water instead of air? Explain.

Q12. A student has two lenses of powers +4 D and −2 D. What is the power of the combination when they are placed in contact?

Q13. Define power of a lens and derive its relationship with focal length. Explain why convex lenses have positive power and concave lenses have negative power.

Q14. Derive the expression for the power of a lens using the lens maker's formula. Show how the power depends on the refractive index of the material and the radii of curvature.

Q15. A person needs corrective lenses. Explain how an optician determines the power of the lens required. What do positive and negative powers indicate about the person's vision defect?

Q16. A person is prescribed spectacles with the following lenses:

Right eye: −2.5 D

Left eye: +1.5 D

(a) Calculate the focal length of each lens.

(b) Identify the type of each lens and the vision defect it corrects.

(c) If the person reads a book placed 25 cm from the eye using the left eye lens, where is the image formed?

Q17. A convex lens has a focal length of 20 cm in air. The refractive index of the lens material is 1.5.

(a) Calculate the power of the lens in air.

(b) Calculate the power of the lens when immersed in a liquid of refractive index 1.6.

(c) Explain why the lens behaves differently in the liquid.

Q18. In your school's health camp, an eye specialist checks the vision of students using a simple lens kit.

(a) A student is unable to see distant objects clearly. The doctor uses a lens of power −0.5 D to correct her vision. Calculate the focal length of this lens and identify the vision defect.

(b) Another student cannot read his textbook comfortably at 25 cm. The doctor prescribes a lens that forms an image at 25 cm when the book is held at a normal reading distance. Calculate the power of the lens required (assume normal reading distance is 25 cm and the student's near point is 50 cm).

(c) The school wants to set up a lens library with lenses of powers +1 D, +2 D, +3 D, −1 D, −2 D, and −3 D. A student picks up a +2 D lens and a −3 D lens and holds them together. Calculate the power and focal length of the combination.

(d) Explain why opticians prefer to specify lens power in dioptres rather than focal length in centimetres when prescribing glasses.