a ray of light enters a rectangular transparent slab at and angle of 45
What happens when a ray of light enters a rectangular transparent slab at an angle of 45 degrees?
Answer: When a ray of light enters a rectangular transparent slab at an angle of 45 degrees, it experiences a phenomenon known as refraction. Let’s walk through the process step-by-step:
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Incident Ray and Angle: The ray hits the surface of the slab at a 45-degree angle to the normal (an imaginary line perpendicular to the surface).
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Refraction: As the ray enters the slab, it changes direction. This bending occurs because light travels at different speeds in different mediums. The degree of bending depends on the refractive index of the slab material.
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Snell’s Law: The relationship between the angle of incidence \theta_1 (45 degrees in this case) and the angle of refraction \theta_2 is given by Snell’s Law:
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)- n_1 is the refractive index of the initial medium (usually air, with n_1 \approx 1).
- n_2 is the refractive index of the slab.
- \sin(\theta_1) and \sin(\theta_2) are the sine of the angles of incidence and refraction, respectively.
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Critical Angle and Total Internal Reflection: If the refractive index of the slab is higher than that of the surrounding medium, and if the angle of incidence inside the slab exceeds a certain value known as the critical angle, total internal reflection can occur. However, with a 45-degree entry and typical conditions, the light will exit the slab unless the slab is extremely thin or the angles are manipulated specially.
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Exit from the Slab: Upon exiting, the light undergoes refraction again at the boundary between the slab and air, bending away from the normal if exiting back into air.
Summary: When a ray of light at 45 degrees enters a transparent slab, it bends due to refraction governed by Snell’s Law. The exact path depends on the refractive index of the slab.