## 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.
**

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