Beyond Beading
Posted on Monday, November 24th, 2008 at 11:07 am
help with refraction ?
1. A dust particle is inside a sphere of refractive index 4/3. If the dust particle is 10 cm from the wall of the 15cm radius bowl, where does it appear to an observer outside the bowl?
2. A parallel beam of light enters a clear plastic bead of diameter 2.50 cm and index 1.44. At what point beyond these beads are these rays brought to a focus ?
Thanks .
1. Dust particle is 5 cm from the centre of the sphere.
Make the principle axis a line from the dust particle to the centre.
draw a normal from the centre to the edge of the sphere ( a radius perpendicular to the axis.)
Draw a ray from the dust to the normal .
The angle of incidence = tan^–1 ( 5 / 15 ) = 18.435˚
The angle of the refracted ray = sin^–1 ( µ . sin 18.435 ) = 24.94˚
Draw the refracted ray backwards till it intercepts the axis. This will be where the image appears to be.
Distance of image from the centre = 15 . sin 24.94 / sin 65.06 = 6.975 cm
The dust grain will seem to be 8.025 cm below the surface.
2. Sorry – this isn’t ( I think ) too hard to do but is too hard for me to describe.
Draw it up . You only need to look at a single ray coming in parallel to the axis. As it crosses the bead, it makes an isosceles triangle with the point it comes out at ( and the angle of incidence = the final angle of refraction. So the geometry is quite easy.
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