Question

What focal length should the reading spectacles have for a person for whom the least distance of distinct vision is 50cm ? ​

Answer 1

Hi !

Solution:- The distance of normal vision is 25 cm . so if a book is at u = - 25cm, it's image should be formed at v = - 50cm. therefore , the disired focal length is given by

1/f = 1/v - 1/u

or, 1/f = 1/-50 - 1/-25 = 1/50

or ,f = + 50cm (convex lens)

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Hope it helps you !!

@Raj❤

Answer 2

Answer:

$\boxed{\underline{\Huge{\texttt{50 cm}}}}$

Explanation:

The distance of distinct vision is 25 cm. As people becomes older, the power of accommodation of their eyes decreases and the distance of distinct vision increases.

The lens formula is $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$, where,

• u is the distance of the object from the lens
• v is the distance of the image from the lens
• f is the focal length of the lens

The distance from the lens to the left is taken as negative and the distance from the lens to the right is taken as positive.

The magnification of the lens = $\frac{h_i}{h_o} = \frac{v}{u}$, where,

• $h_i$ is the height of the image, and,
• $h_o$ is the height of the object.

The distance above the principal axis is taken as positive and the distance below the principal axis is taken as negative.

In this case, the distance of distinct vision is given as 50 cm. Therefore,  when an object is placed at a distance of 25 cm, it appears to the eye that the object is at a distance of 50 cm.

Hence, we use a lens such that for an object at a distance of 25 cm, the image is at a distance of 50 cm.

As per the sign convention given above, u = -25 cm and v = -50 cm.

Using the lens formula, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\implies -\frac{1}{50} + \frac{1}{25} = \frac{1}{f}\\ \implies \frac{1}{f} = \frac{1}{50} \Rightarrow f = 50 \text{ cm}$

Since the sign of f is positive, we conclude that the focus of the lens should be in the direction opposite to that of the object.

Therefore, We should use a convex lens with focal length 50 cm.