Blue light of wavelength 440 nm is incident on two slits separated by 0.30 mm. Determine (a) the

step 1 Okay, so for question three. So, okay, blue light of wavelengths, which is 440 nanometers, is in

Blue light of wavelength 440 nm is incident on two slits...

Key Concepts

Spatial Separation of Interference Fringes

The spatial separation of interference fringes on a screen is the distance between successive bright (or dark) fringes. This separation is determined by the angular deflection and the distance from the slits to the screen. Using the small angle approximation, the linear displacements on the screen can be estimated by multiplying the angular deflection by the distance to the screen, linking the microscopic interference effects to observable patterns on a macroscopic scale.

Screen Distance and Fringe Geometry

The distance from the slits to the screen plays a key role in the magnification of the interference pattern. A larger distance enhances the spatial separation between fringes, making the pattern easier to observe and measure. This relationship is critical in designing experiments and devices that rely on interference patterns, as it connects the experimental setup to the observed geometrical distribution of light.

Angular Deflection in Interference Patterns

Angular deflection refers to the angle at which a particular interference fringe (bright or dark) is observed relative to the central maximum. This concept is important as it connects the physical parameters of the experimental setup (such as slit separation and wavelength) to the geometry of the interference pattern. The angular position, derived from conditions of constructive interference, provides a direct measure of the deviation of light from the original propagation direction.

Young's Double-Slit Interference

This concept involves the observation of interference patterns produced when a coherent light source passes through two closely spaced slits. The interference of light waves from the two slits leads to the formation of bright and dark fringes, with bright fringes occurring due to constructive interference and dark fringes due to destructive interference. This principle is fundamental to understanding the wave nature of light and has wide applications in optics and experiments demonstrating wave interference.

Constructive Interference

Constructive interference occurs when two light waves from separate slits combine in phase, meaning that their path difference is an integer multiple of the wavelength. This condition, typically represented by the equation d sin(?) = m? (where d is the slit separation, ? is the angle of the fringe relative to the central maximum, m is the order of the fringe, and ? is the wavelength), is essential for determining the location of bright fringes in an interference pattern.

Transcript

00:01 Okay, so for question three.

00:04 So, okay, blue light of wavelengths, which is 440 nanometers, is incident on two slits, separated by 0 .3 millimeter.

00:14 So for the first question, we need to determine the angular deflection to the center of third order bright band.

00:21 So that's actually a formula for the angular deflection, which is given here.

00:27 Sign theta m equals m landa over d.

00:29 And the m here means the order and we are looking for the angle deflection to the center of a third order byband so m is equal to 3 and the land is a wavelength and we already know the wavelengths from the question which is 440 nanometer and 1 nometer is 10 to negative 9 meter so after all the conversion we get at 440 nanometer it's equal to 4 .4 times 10 to negative 7 meter and then d here is a separation between two slits, which is 0 .3 millimeter, and 1 millimeter is 10 to negative 3 meter.

01:08 So 0 .3 millimeter is equal to 3 times 10 to negative 4 meters.

01:14 So we get all the data for different elements, and we get cyanidea3 equals 3 times 4 .4 times 10 to negative 7 meter, divided by 3 times negative 4 meter.

01:29 And we get the value is 0 .0044.

01:36 And that's the value for angle deflection.

01:40 But actually, we need to find angles because we'll need it for later questions.

01:52 It won't hurt us to calculate the angle from some function.

01:58 All we need to do is just plugging the way we got from the previous equations into arc sign, or we call it inverse sign function, and we get the angle is 0 .25 degree.

02:13 And for question b, we need to find the spatial separation from the zero's order band when the line is projected on the screen, located 3 meter from the slits.

02:23 And we are so lucky, and there's also a formula for such questions.

02:29 So for the spatial separation from 0's order to m order band, the formula is this.

02:38 It's ym equals m times capital l times slander divided by d.

02:43 And m here is also means the order.

02:48 And capital l here means the distance from the slit to a screen.

02:51 And it was given.

02:53 It's 3 meter.

02:54 Let's take look.

02:56 It says 3 meter from the slit.

02:57 So it's 3 meter.

02:59 And atlanta is just the wavelength.

03:01 We already get it, which is 4 .4 times 10 to the negative 7 meter, which is 440 .9.

03:06 And these just a separation with two slits, which is three times 10 to a negative 4 meter, 0 .3 millimeters.

03:14 The reason why we convert two meters is for the simplification for calculation, so we can calculate it easier...

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