A student designs an experiment to replicate Young’s double slit demonstration. The student uses a candle as a light source, with a piece of coloured filter paper to produce monochromatic light. They then consider additional apparatus required in order to observe an interference pattern.
a)
Sketch a diagram, labelling all apparatus, as well as any important quantities, to show the setup the student should use to produce and observe an interference pattern.
The student labels the two slits on the double-slit grating slit X and slit Y. The student then paints over slit X, such that the intensity of light emerging from it is 50% of that emerging from slit Y.
(b)
Discuss the effects this change will have on the student’s observations.
On the diagram from part (a), draw the continuation of the path of the ray of light until it emerges back into the air, labelling the values of the angles between the ray and any normals.
The prism is rotated and one side is coated with a film of transparent gel. A ray of light strikes the prism, at an angle of incidence of 38°, and continues through the glass to strike the glass–gel boundary at the critical angle.
A soap bubble is known as a ‘thin film’. There is a thin layer of water trapped between soap molecules on either side.
Light that hits the bubble behaves in very predictable ways, resulting in visually interesting and colourful effects.
Blue light of wavelength 400 nm is incident at an angle on a bubble where it splits into a ray that is reflected (ray ) and a ray which refracts into the bubble (ray ). Ray reflects from the other side of the film, and then leaves the bubble again.
Upon reflection, ray undergoes a phase shift of radians. Ray does not undergo any phase shift upon reflection.
a) Determine an expression for the path difference between ray and ray , justifying your answer.
Anti-reflective coatings use thin-film interference effects to make it appear that light is not reflected from the surface and instead passes straight through it. A simplified version of anti-reflective coated glass is shown in the diagram:
The coating is designed such that there is a phase shift of radians at the first boundary (between the air and the coating) as well as at the second boundary (between the coating and the glass).
(d)
By considering the conditions for constructive or destructive interference, discuss the limitations of this design.
The tube of an endoscope behaves like an optical fibre to examine the interior of the body for medical diagnosis. One end of the fibre is illuminated and an image of the inside of the stomach is viewed by the doctor.
(a)
Draw on the picture the complete path of the light from the illumination to the doctor.
The diagram shows a cross–section through an optical fibre used in an endoscope. The critical angle is 7% lower than the 75º angle to the normal at the core–cladding boundary. The refractive index of the cladding is 1.4.
(b)
Calculate the angle of incidence at the air–core boundary.
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