Question

A person needs a lens of power -5.5 dioptres for correcting his distant vision. For correcting his near vision, he needs a lens of power + 1.5 dioptres. What is the focal length of the required for correcting (i) distant vision, and (ii) near vision ?
A.
B.
C.
D.

Answer 1

(i) for distant vision : Power of lens ,P=-5.5D
Now ,Power , `P=(1)/(f"(in metres)")" "("where f=Focal length ")`
SO, `-5.5=(1)/(f)`
And , `f=(1)/(-5.5)m`
Or , `f=-(1)/(5.5)xx100cm`
So, Focal length f=-18.18 cm `" "`(or-18.2cm)
thus the focal length of lens required for correcing distant vision is, - 18.2 cm. Minus sign of focal length tells us that it is a concave lens.
(ii) for near vision : power of lens, P=+ 1.5D
Now, Power , `P=(1)/(f"(metres)") `
So `+1.5 =(1)/(f)`
And `f=(1)/(+1.5)m`
Or, `f = +(1)/(1.5)xx100cm`
So, focal length, f = + 66.66 cm (or + 66.7 cm)
Thus the focal length of lens required for required for correcting near vision is +66.7 cm Plus sign of focal length tells us that it is a convex lens.