The least distance of distinct vision of a person is 50 cm. He wants to read a book placed at 25 cm. The focal length of the spectacles would be:

The correct option is +50 cm.

Step-by-Step Explanation:

1. Identify the given values and understanding the problem:
The person has hypermetropia (farsightedness), where the least distance of distinct vision (near point of the defective eye) is shifted further away.
The near point of the person's eye is:
$d=50\text{cm}$
This means the person cannot see objects clearly if they are closer than 50 cm. Any virtual image must be formed at this distance for the person to see it clearly. Thus, the image distance ($v$) should be:
$v=-50\text{cm}$ (negative sign represents that the image is virtual and on the same side as the object).

The person wants to read a book placed at the normal near point:
$u=-25\text{cm}$ (the object distance, also negative according to sign convention).

2. Apply the Lens Formula:
The relationship between focal length ($f$), object distance ($u$), and image distance ($v$) is given by the lens formula:

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

3. Substitute the values:

$\frac{1}{f}=\frac{1}{-50}-\frac{1}{-25}$

$\frac{1}{f}=-\frac{1}{50}+\frac{1}{25}$

Taking the common denominator, which is 50:

$\frac{1}{f}=\frac{-1+2}{50}$

$\frac{1}{f}=\frac{1}{50}$

Reciprocating both sides:
$f=+50\text{cm}$

The positive focal length confirms that a convex (converging) lens of focal length +50 cm is required to correct this vision defect.