Final answer:
The direction of light as it passes through the prism can be predicted using Snell's law and properties of refraction. The angle between the exiting light ray and the 'normal' can be found via the same laws, taking note of the difference in refractive indices between the mediums. The angle that facilitates total internal reflection can be calculated using the critical angle formula.
Step-by-step explanation:
To address part a) of your question, we can make use of Snell's law, which states that the ratio of the sine of the angles of incidence and refraction is equivalent to the ratio of propagation speed in the two media, or in this case, equivalent to the ratio of the indices of refraction. With a higher index of refraction (n=1.5), the light entering the prism from air will bend towards the normal line when it enters the prism (side AB), and bends away from the normal line when it exits the prism (side BC). This is due to the prism's higher refractive index causing the light to travel slower inside the prism than it does in the air.
For part b), you would use Snell's law again to calculate the angle between the exiting light ray and the normal line (which appears to be the dashed line in your question). Given the index of refraction of the prism and air, along with the angle of incidence, you can solve for the angle of refraction, which should provide this angle.
Finally, for part c) to achieve total internal reflection at side BC, the angle at corner B must be such that the incident angle of light at side BC is greater than the critical angle for the given refractive index. The critical angle can be calculated using the formula: critical angle = arcsin(n2/n1), where n2 is the refractive index of air and n1 is the refractive index of the prism material.
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