Which of the following interface combinations has the...

Which of the following interface combinations has the smallest critical angle?
a) light traveling from ice to diamond
b) light traveling from quartz to Lucite
c) light traveling from diamond to glass
d) light traveling from Lucite to diamond
e) light traveling from Lucite to quartz

Key Concepts

Total Internal Reflection

Total internal reflection occurs when light traveling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle, resulting in all of the light being reflected back into the denser medium. This concept is essential for understanding various optical phenomena and is highly dependent on the relative indices of refraction of the materials at the interface.

Critical Angle

The critical angle is the minimum angle of incidence in the denser medium at which light is totally internally reflected at the interface with a less dense medium. It is determined by the ratio of the indices of refraction of the two media and is only defined when light travels from a medium with a higher index of refraction to one with a lower index.

Snell's Law

Snell's Law is the fundamental law governing the refraction of light at an interface between two media. It relates the angles of incidence and refraction to the indices of refraction of the two media, providing the mathematical basis for calculating the critical angle where total internal reflection occurs.

Index of Refraction

The index of refraction quantifies how much a medium slows down light compared to its speed in vacuum. Differences in indices of refraction between media determine the bending of light and the conditions for total internal reflection, as a higher index in the initial medium compared to the second medium is necessary for a well-defined critical angle.

Transcript

00:01 To the chapter geometric optics in which we have to determine the combination having smallest critical angle.

00:07 So for option a, we have light traveling from ice to diamond, ice to diamond.

00:14 So the critical angle of incident theta c, it is equals to arc sine n2 by n1.

00:22 N1 is the refractive index from where the race incidenting and n2 is the refractive index of the medium where ray is going.

00:31 So this is 1 and this is 2.

00:33 So refractive index of the ice is equals to 1 .310 and for the diamond it is 2 .417.

00:41 So hence we can say that the ray is going from lower refractive index to higher refractive index.

00:49 So the critical angle is not possible.

00:52 Critical angle is not possible.

00:55 Because we will get this value greater than 1 at sine in.

00:59 Inverse of greater than one value is not possible.

01:01 So now moving to the option b in which we have from quads to quartz to lew site.

01:10 So the refractive index of the quartz is equals to 1 .5 double four and for the lew site it is 1 .5.

01:18 So again we have refractive index here it is possible.

01:22 So from here after substituting value, so theta c it will be equals to arc sign 1 .5 divided by 1 .5 double 4 and this will be obtained as this will be equals to 76 .3 degree...

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