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**Introductory Exercise 29.1**

**Ques 1: In YDSE, D = 1.2 m and d = 0.25 cm. The slits are illuminated with coherent 600 nm light. Calculate the distance y above the central maximum for which the average intensity on the screen is 75% of the maximum.Sol:**

= 48 Ã— 10

Sol:

This is the condition for destructive interference.

Sol:

So, I

Let A

Then A

and I

Now, I = I

Sol:

path difference is equivalent to 180Â° phase difference.

Hence, maximas and minimas interchange their positions.

Sol:

Highest integer in Î”6.

Sol:

**ExercisesFor JEE Main**

**Subjective QuestionsEnergy Distribution in Interference**

Sol:

A

âˆ´

Sol:

= 1.25 Ã— 10

Sol:

âˆ´

or

âˆ´

(a) At a point in the pattern where the phase difference between the waves from the two slits is 60Â°, what is the intensity?

(b) What is the path difference for 480 nm light from the two slits at a point where the phase angle is 60Â°?

Sol:

(b) 60Â° phase difference is equivalent to Î»/6 path difference.

Ques 6: Two coherent sources A and B of radio waves are 5.00 m apart . Each source emits waves with wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if any, from A is the interference (a) constructive, (b) destructive?

At a distance, where path difference is Î»/2 or 3m destructive interference will be obtained.

At P

At P

Sol:

Î”x = (BP - AP) = (9 - 2x) = nÎ»

âˆ´

Now, substituting n = 1, 2, ...... etc. We can find different values of x.

x

x

and

x

Similarly we will get three points at same distance from other point B.

Ques 8: Coherent light from a sodium-vapour lamp is passed through a filter that blocks every thing except for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. What is the wavelength?

= 0.589 Ã— 10

Sol:

â‰ˆ 0.014Â°

Sol:

Fringe width

= 10

Sol:

= 2.0 Ã— 10-6 m = 2.0 Î¼m

Sol:

= 7.2 Ã— 10

Sol:

= 8.33 Ã— 10

Sol:

â‡’ Î»

Sol:

âˆ´

âˆ´ y

= 35 tan 8.78Â° = 5.41 cm

âˆ´

âˆ´ Î¸

y

= 35 tan 27.27Â°

= 18 cm

Î”y = y

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