Question

An old lady cannot see clearly upto a distance of 0.075cm from her eyes . An optician corrects her vision. Guess the power of lens prescribed to her
​

Answer 1

CORRECT QUESTION :-

An old lady cannot see clearly upto a distance of 0.75 cm from her eyes. An optician corrects her vision. Guess the power of lens prescribed to her .

GIVEN :-

An old lady cannot see clearly upto a distance of 0.075 cm from her eyes.

Her nearest point = 0.75 cm.

TO FIND :-

The power of lens prescribed to her .

SOLUTION :-

We know, the nearest vision of our normal eye is 25 cm.

As 0.75 cm > 25 cm, so she can't see nearer objects. This means she is suffering from hypermetropia.

Now,

u = -0.75 cm

v =

​By using the Lens formula :-

$\displaystyle{\sf{\frac{1}{v}-\frac{1}{u}=\frac{1}{f} }}\\\\\displaystyle{\sf{\implies \frac{1}{\infty}-\frac{1}{-0.75}=\frac{1}{f} }}\\ \\\displaystyle{\sf{\implies 0+\frac{1}{0.75}=\frac{1}{f} }}\\\\\displaystyle{\sf{\implies \frac{1}{0.75}=\frac{1}{f} }}\\\\\boxed{\displaystyle{\sf{\implies f=1.33 }}}$

We know, power is the reciprocal of the focal length.

⇒Power = 1/1.33

⇒Power = 0.75 Dioptre

◘ So, the old lady was prescribed with a convex lens with power 0.75 D.

Answer 2

QUESTION

An old lady cannot see clearly upto a distance of 0.75 cm from her eyes. An optician corrects her vision. Guess the power of lens prescribed to her .

ANSWER

Given

Nearest point = 0.75 cm

$\implies u = -0.75 \ cm\\v = \infty$

0.75 cm > 25 cm

=> The lady is suffering from hypermetropia

Hypermetropia is a condition where a person is long - sighted. They can see faraway objects clearly than the nearby objects.

LEN'S FORMULA

$\dfrac{1}{f} = \dfrac{1}{v} -\dfrac{1}{u}$

Substituting, the values we get,

$\implies \dfrac{1}{\infty} - \dfrac{1}{-0.75} = \dfrac{1}{f}$

$\implies0 - \dfrac{1}{-0.75} = \dfrac{1}{f}$

$\implies \dfrac{1}{0.75} = \dfrac{1}{f}$

Now, Power is the reciprocal of focal length

$\boxed{\boxed{\bold{Therefore, \ the \ power \ of \ lens \ prescribed \ to \ her \ is \ 0.75 \ D}}}}}}}}}}}$