Power of a Lens - UNSOLVED PRACTICE SET

Q7. Define the power of a lens. Write the formula and state the SI unit. Why is the focal length in the formula always expressed in metres?

Q8. Calculate the power of:
(a) a convex lens of focal length 50 cm, and
(b) a concave lens of focal length 40 cm. Include correct signs.

Q9. Two lenses with powers +4 D and +2 D are placed in contact. What is the combined power? What is the combined focal length?

Q10. An optometrist prescribes +3.5 D glasses for a student.
(a) What eye defect does the student have?
(b) What type of lens is used?
(c) Find the focal length of the prescribed lens.

Q11. A combination of lenses has total power +6 D. One lens has power +10 D. What is the power and focal length of the second lens?

Q12. Explain why powerful lenses have short focal lengths and weak lenses have long focal lengths. Give one practical example from everyday life. 

Q13. Define the power of a lens and explain its significance in optics and everyday life. Your answer must include:
(a) the formula P = 1/f and why f must be in metres,
(b) the sign convention - why convex lenses have positive power and concave lenses have negative power,
(c) the unit dioptre - define 1 D,
(d) the formula for combined power of lenses in contact: P = P? + P?, and
(e) how the concept of power is used in spectacle prescriptions with two real Indian examples.

Q14. A student in Pune goes for an eye test. The optometrist prescribes: Right eye: ?1.5 D. Left eye: +2.0 D.
(a) What eye defect does each eye have?
(b) What type of lens is needed for each eye?
(c) Find the focal length of each prescribed lens.
(d) The student later uses a reading glass of +2.5 D in addition to her left-eye spectacle. If both lenses are in contact, what is the combined power and focal length?
(e) Explain why a person with myopia sees distant objects blurry but near objects clearly.

Q15. Analyse the relationship between power, focal length, and lens strength.
(a) A lens maker produces three lenses with focal lengths 10 cm, 25 cm, and 50 cm (all convex). Calculate the power of each.
(b) Which is the strongest converging lens?
(c) A ?5 D lens and a +8 D lens are placed in contact - find combined power and focal length.
(d) Is the combined lens converging or diverging?
(e) An eye surgeon inserts an intraocular lens (IOL) of +20 D to replace a damaged natural lens. What is its focal length? Why must this power be very precise?

Q16. A spectacle lens has a focal length of ?40 cm.
(a) What type of lens is this?
(b) Calculate its power.
(c) An ophthalmologist combines this lens with a +5 D lens. Find the net power.
(d) Find the net focal length.
(e) Is the combination converging or diverging?

Q17. Three lenses with focal lengths +20 cm, +50 cm, and ?25 cm are placed in contact.
(a) Convert each focal length to metres and calculate power with sign.
(b) Find the total combined power.
(c) Find the combined focal length.
(d) Is the combination convergent or divergent?
(e) What single lens could replace all three? Describe it.

Q18. A person can see clearly up to 1 m but cannot focus on distant objects.
(a) Name the eye defect.
(b) Using lens formula: object at infinity must form image at ?100 cm (the far point). Use 1/v ? 1/u = 1/f with u = ?? and v = ?100 cm to find f.
(c) Calculate the power of the corrective lens.
(d) What type of lens is prescribed?
(e) After correction, the person also needs a reading glass of +2 D for near work. If placed in contact with the corrective lens, what is the net power?