Question

How does focal length of a lens change when red light incident on it is replaced by violet light? Give reason for your answer.

Answer 1

Answer:

Let us assume that width of each slit = a.

In a double slit experiment, the separation between Maxima (m) is given as

y = m(Lambda) D/d

D = distance between screen and slit

d = Separation between the slits.

The angular separation between m Maxima is described as

Ф = y/D = m(Lambda) D/(D*d) = m(Lambda)/d

We can derive the angular separation between 10 bright fringes by substituting m = 10

Theta = 10(Lambda)/d = 10(Lambda)/1 = 10(Lambda)  (d = separation between the slits = 1 mm)

Angular width of the central maximum in the single slit differential pattern of width ‘a’ is described as  

2(Ф1) = 2(Lambda)/a

From the question, it is clear that 10 maxima of the double slit pattern is formed within the central maximum of the single slit pattern.

Hence above 2 equations can be equated.

10(Lambda) = 2(Lambda)/a

∴ a = 2/10 = 0.2mm.

The width of each slit = 0.2mm.

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Explanation:

Answer 2

Answer:

Focal length of the convex lens increases with the increase in wavelength. We know wavelength of red is more than the wavelength of violet. So, as the wavelength decreases the focal length also decreases.