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 dioptre. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?

 

Answer

We know that, 

Power of a lens = 1/Focal Length

Therefore, 

Focal Length = 1/ Power of the lens

 

Note : Here power is in m

 

(i) distant vision

For distant vision,

Power of the lens = −5.5 D

Focal length(m) = 1/ Power of the lens

                      = 1/ (−5.5)

                      = −10/55

                      = −2/11

                      = -0.1818 m

                      = −0.1818 × 100 cm

                      = −18.18 cm

                      = −18.2 cm

 

Focal length of the lens required for correction for distant vision is −18.2 cm

Since the focal length is negative, the lens used is concave lens.

 

(ii) near vision

For near vision,

Power of the lens = 1.5 D

Focal length(m) = 1/ Power of the lens

                      = 1/ (1.5)

                      = 10/15

                      = 2/3

                      = 0.667 m

                      = 0.667 × 100 cm

                      = 66.7 cm

 

Focal length of the lens required for correction for near vision is 66.7 cm

Since the focal length is positive, the lens used is convex lens.

  1. Class 10
  2. Chapter 11 Class 10 - Human Eye and Colourful World

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.