This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: In Young's double slit experiment, the number of fringes observed in the field of view is small with longer wavelength of light and is large with shorter wavelength of light.
Statement-2: In the double slit experiment the fringe width depends directly on the wavelength of light.

In Young's double slit experiment, we need to evaluate Statement-1 and Statement-2.

First, recall the formula for fringe width, denoted by $$\beta$$. The fringe width is given by:

$$\beta = \frac{\lambda D}{d}$$

where $$\lambda$$ is the wavelength of light, $$D$$ is the distance between the slits and the screen, and $$d$$ is the separation between the two slits.

Statement-2 claims that the fringe width depends directly on the wavelength of light. From the formula, if $$D$$ and $$d$$ remain constant, then $$\beta$$ is proportional to $$\lambda$$, meaning $$\beta \propto \lambda$$. Therefore, Statement-2 is true.

Now, Statement-1 claims that the number of fringes observed in the field of view is small with longer wavelength and large with shorter wavelength. The field of view refers to a fixed region on the screen with a constant width, say $$W$$. The number of fringes, denoted by $$N$$, is approximately the total width of the field of view divided by the fringe width. So:

$$N = \frac{W}{\beta}$$

Substituting the expression for $$\beta$$:

$$N = \frac{W}{\frac{\lambda D}{d}} = \frac{W d}{\lambda D}$$

Assuming $$W$$, $$d$$, and $$D$$ are constant for the setup, then $$N \propto \frac{1}{\lambda}$$. This means that as the wavelength $$\lambda$$ increases, the number of fringes $$N$$ decreases, and as $$\lambda$$ decreases, $$N$$ increases. Therefore, with longer wavelength, the number of fringes is small, and with shorter wavelength, it is large. Hence, Statement-1 is true.

Now, we must determine if Statement-2 correctly explains Statement-1. Statement-2 states that fringe width is directly proportional to wavelength, which is correct. The number of fringes decreases with increasing wavelength because the fringe width increases, leading to fewer fringes fitting within the fixed field of view. However, for this explanation to hold, we must assume that the field of view width $$W$$ is constant and does not depend on wavelength. Statement-2 does not mention the field of view or its constancy. Therefore, while Statement-2 is true and related, it is not by itself a complete explanation for Statement-1 without the additional implicit assumption of a fixed field of view.

Hence, both statements are true, but Statement-2 is not the correct explanation for Statement-1.

So, the answer is Option C.