Question 116: Wave Optics

Question

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 $$\mathop A\limits^o $$ is :-

Accepted Answer

In the double-slit experiment, the position of a bright fringe is given by the formula :
$y = \frac{{m\lambda L}}{{d}}$,
where :
m is the order of the fringe (1 for the first bright fringe, 2 for the second, etc.)
$\lambda$ is the wavelength of the light (in meters)
L is the distance from the slits to the screen (in meters)
d is the distance between the slits (in meters)
We need to find the difference in position between the first and third bright fringes. So, we find the position of both and subtract the position of the first from the position of the third :
$y_3 = \frac{{3\lambda L}}{{d}}$
$y_1 = \frac{{\lambda L}}{{d}}$
Then, the difference between the third and the first bright fringes is :
$y_3 - y_1 = 2\frac{{\lambda L}}{{d}}$
Now, let's plug the given values: $\lambda = 5890 \,ÃÂ = 5890 	imes 10^{-10} \, m$ (since 1 ÃÂ = $10^{-10}$ meters), L = 0.5 m, and d = 0.5 mm = 0.5 $	imes 10^{-3}$ m :
$$ y_3 - y_1 = 2 	imes \frac{5890 	imes 10^{-10} \, 	ext{m} 	imes 0.5 \, 	ext{m}}{0.5 	imes 10^{-3} \, 	ext{m}} = 1178 	imes 10^{-6} \, 	ext{m} $$
So, the correct answer is 1178 $	imes 10^{-6}$ m, which corresponds to Option B.

Answer

1178 $$	imes$$ 10
$$-$$9
m

Answer

1178 $$	imes$$ 10
$$-$$6
m

Answer

1178 $$	imes$$ 10
$$-$$12
m

Answer

5890 $$	imes$$ 10
$$-$$7
m

Wave Optics

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 $\mathop A\limits^o $ is :-

Choose the correct answer: