Question

A person cannot read newspaper placed nearer than 50 cm fromm his eyes calculate its power and assume that the near point for the normal eye is 25 cm

Answer 1

Given :-

• near point of person's eye = 50 cm
• near point of normal eye = 25 cm

To find :-

• Power of lens required for correction

Formula used :-

• Lens formula

$\boxed{\rm{\frac{1}{f}=\frac{1}{v}-\frac{1}{u}}}$

( where f is the focal length of lens , u is the position of object and v is the position of image)

• Formula for finding the power of lens using focal length

$\boxed{\rm{P=\frac{1}{f}}}$

( where P is the power and f is the focal length )

Note: while finding power  focal length should be in metres .

Solution :-

According to the given information

⇢ position of object , u = - 25 cm

⇢ position of image , v = -50 cm

⇢ Let, focal length of lens required = f

Using Lens formula

$\rm{\frac{1}{f}=\frac{1}{-50}-(\frac{1}{-25})}\\\\\rm{\frac{1}{f}=\frac{1-2}{-50}=\frac{-1}{-50}}\\\\\underline{\large{\rm{f=50\:cm}}}$

Converting the focal length in cm into metres

f = 50 cm

$\rm{f=\frac{50}{100}\;m=0.5\;m}$

Finding the power of lens required

$\rm{P=\frac{1}{f}=\frac{1}{0.5}}\\\\\underline{\large{\rm{P=+\;2\;D}}}$

Hence, the power of lens will be + 2 Dioptre.

Since, power is positive hence lens will be Converging .