Question 29

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t = 10$$ $$\mu$$m and refractive index $$\mu = 1.2$$ is inserted infront of slit $$S_1$$. The experiment is conducted in air ($$\mu = 1$$) and uses a monochromatic light of wavelength $$\lambda = 500$$ nm. Due to the insertion of the plate, central maxima is shifted by a distance of $$x\beta_0$$. $$\beta_0$$ is the fringe-width before the insertion of the plate. The value of $$x$$ is ______.

Correct Answer: 4

The shift in the position of the central maxima ($$\Delta y$$) is given by:

$$\Delta y = \frac{D}{d}(\mu - 1)t$$

The fringe width $$\beta_0$$ is defined as $$\beta_0 = \frac{\lambda D}{d}$$

$$x \beta_0 = \frac{D}{d}(\mu - 1)t$$

$$x \left( \frac{\lambda D}{d} \right) = \frac{D}{d}(\mu - 1)t$$

$$x = \frac{(\mu - 1)t}{\lambda}$$

$$x = \frac{(1.2 - 1) \times 10 \times 10^{-6}}{500 \times 10^{-9}}$$

$$x = \frac{20}{5} = 4$$

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