Question

a person needs a lens of power 5.5 diaptre for correcting his distant vision he needs needs a lens of power +1.5 diaptre what is the focal length of the length required for correcting first one distant vision second one near vision​

Answer 1

Correct question:

A person needs a lens of power -5.5 dioptre 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?

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

A person needs two lenses for:

• Distant vision, which is -5.5 D.
• Near vision, which is +1.5 D.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

We need to calculate the focal length of:

• Distant vision lens.
• Near vision lens.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

We can use the power-focal length relation, i.e.,

$\boxed{\sf{\green{Focal \ length (f)=\dfrac{1}{Power(D)} }}}$

CASE 1:

The power is -5.5 D.

Focal length can be determined as:

$\sf{\red{f=\dfrac{1}{p} }}$

Substitute the values.

$\to \sf{\red{f=\dfrac{1}{-5.5} }}$

$\boxed{\sf{\green{f=-0.18 m.}}}$

CASE 2:

The power is +1.5 D.

Focal length can be determined as:

$\sf{\red{f=\dfrac{1}{p} }}$

Substitute the values.

$\to \sf{\red{f=\dfrac{1}{+1.5} }}$

$\boxed{\sf{\green{f=0.67 m.}}}$

ANSWER:

• Distant vision: -0.18 m.
• Near vision: 0.67 m.