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# Some Waves Questions watch

1. I am struggling with some waves questions, any help is appreciated.

Part 1

When light hits an interface of two materials of differing refractive index, refraction can take place. Sketch this effect, labelling the two regions, the angle of incidence and refraction, and the two refractive indices.

A layer of oil floats on top of a layer of water. At the bottom is a point source of light, which emits in all directions equally.

Calculate the critical angle for the water-oil interface. Calculate the critical angle for the oil-air interface.

Using the depths of the two materials along with the two critical angles, calculate the distance labelled x in the above diagram.

Part 2

A microwave source emits monochromatic plane waves at a double slit. The slits are separated by 0.25 m, and a screen, 1.0 m away from the slits measures the resulting diffraction pattern.
From this diffraction pattern, the fringe width (distance from one maximum to another) is 0.3 m. The speed of microwaves in air is 3.0×108 ms−1.

Sketch the resulting diffraction pattern on the screen.

Calculate the wavelength and frequency of the microwaves using the Young’s slit formula.

Calculate the wavelength and frequency of the microwaves using trigonometry to calculate the path difference.

Note, in the trigonometric case, you can use the position of the point labelled x on the diagram to correspond to a minimum (cancellation of the waves when they arrive at this point).
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2. (Original post by Crasterlover)
I am struggling with some waves questions, any help is appreciated.

Part 1

When light hits an interface of two materials of differing refractive index, refraction can take place. Sketch this effect, labelling the two regions, the angle of incidence and refraction, and the two refractive indices.

A layer of oil floats on top of a layer of water. At the bottom is a point source of light, which emits in all directions equally.

Calculate the critical angle for the water-oil interface. Calculate the critical angle for the oil-air interface.

Using the depths of the two materials along with the two critical angles, calculate the distance labelled x in the above diagram.

Part 2

A microwave source emits monochromatic plane waves at a double slit. The slits are separated by 0.25 m, and a screen, 1.0 m away from the slits measures the resulting diffraction pattern.
From this diffraction pattern, the fringe width (distance from one maximum to another) is 0.3 m. The speed of microwaves in air is 3.0×108 ms−1.

Sketch the resulting diffraction pattern on the screen.

Calculate the wavelength and frequency of the microwaves using the Young’s slit formula.

Calculate the wavelength and frequency of the microwaves using trigonometry to calculate the path difference.

Note, in the trigonometric case, you can use the position of the point labelled x on the diagram to correspond to a minimum (cancellation of the waves when they arrive at this point).
where are you getting stuck?

looks like you've been provided a deliberately misleading diagram... I suggest you sketch your own.

for rays going from a material with a higher refractive index into a material with a lower refractive index, the angle (measured from the normal) gets bigger.

sin θ2/ sin θ1 = n1/n2

critical angle is when θ2 = 90... so sin θ2 = 1.0

I presume it wants you to find the maximum value possible for X though it doesn't seem to say so - is there a bit of question missing.
3. (Original post by Joinedup)
where are you getting stuck?

looks like you've been provided a deliberately misleading diagram... I suggest you sketch your own.

for rays going from a material with a higher refractive index into a material with a lower refractive index, the angle (measured from the normal) gets bigger.

sin θ2/ sin θ1 = n1/n2

critical angle is when θ2 = 90... so sin θ2 = 1.0

I presume it wants you to find the maximum value possible for X though it doesn't seem to say so - is there a bit of question missing.
To clarify the light travelling from the oil to air is supposed to be at the critical angle.
4. (Original post by Crasterlover)
To clarify the light travelling from the oil to air is supposed to be at the critical angle.
I'd start by calculating the angles from the oil air boundary and work backwards towards the light source... and then get the lengths by constructing right angle triangles & using trig

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