Question

The optician’s prescription for a spectacle lens is marked $+0.5D$. What is the:
A. Nature of spectacle lens?
B. Focal length of spectacle lens?

Answer 1

Hint : To solve these types of questions must remember that whether a positive power means that the lens of the spectacle is converging or diverging. And to calculate the focal length of the spectacle lens we must remember the formula that can be used to calculate the focal length of the lens with the help of the given power.

Complete step-by-step solution:
Since the power of the spectacle lens is given in positive hence, we can conclude that the lens is a converging one.
Now we may proceed on to find the focal length of the spectacle lens. According to the formula, the focal length $(f)$ of the spectacle lens is the inverse of its power $(p)$. Hence, we can write the formula as follows:
$f=\dfrac{1}{p}$
Now since we know the formula to calculate the focal length of the spectacle lens, we can substitute the values in the formula and find out the answer. The power of the spectacle lens is given as $+0.5D$ and on substituting the values in the formula, we get:
$\begin{aligned} & f=\dfrac{1}{0.5} \\\ & \therefore f=2\text{ m} \\\ \end{aligned}$
Thus, the focal length of the spectacle lens will be $2\text{ m}$. Since the lens is a converging one hence its focal length will also be positive.

Note: A convex lens is known to converge the light rays while a concave lens would diverge the light rays away from the principal axis. As discussed above, since the power of the spectacle lens is positive hence it would be a converging lens which implied that the lens would be a convex one.