Light is incident in air at an angle (Fig. P33.54) on the upper surface of a transparent plate,

Name: Problem 54, Chapter 33: University Physics with Modern Physics
Uploaded: 2020-11-09T16:18:27-08:00
Duration: 6 min 48 s
Channel: Khoobchandra Agrawal

step 1 Hello everyone in the given figure if we apply the SNAL slug it would n sine of theta a to be eq

Question

Light is incident in air at an angle $\theta_a$ ($\textbf{Fig. P33.54}$) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. (a) Prove that $\theta_a = \theta'_a$. (b) Show that this is true for any number of different parallel plates. (c) Prove that the lateral displacement $d$ of the emergent beam is given by the relationship $$d = t {\mathrm{sin} (\theta_a - \theta'_b) \over \mathrm{cos} \theta'}$$ where $t$ is the thickness of the plate. (d) A ray of light is incident at an angle of 66.0$^\circ$ on one surface of a glass plate 2.40 cm thick with an index of refraction of 1.80. The medium on either side of the plate is air. Find the lateral displacement between the incident and emergent rays.

   Light is incident in air at an angle $\theta_a$ ($\textbf{Fig. P33.54}$) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. (a) Prove that $\theta_a = \theta'_a$. (b) Show that this is true for any number of different parallel plates. (c) Prove that the lateral displacement $d$ of the emergent beam is given by the relationship $$d = t {\mathrm{sin} (\theta_a - \theta'_b) \over \mathrm{cos} \theta'}$$ where $t$ is the thickness of the plate. (d) A ray of light is incident at an angle of 66.0$^\circ$ on one surface of a glass plate 2.40 cm thick with an index of refraction of 1.80. The medium on either side of the plate is air. Find the lateral displacement between the incident and emergent rays.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 33, Problem 54

Instant Answer

Solved by Expert Khoobchandra Agrawal

11/09/2020

Step 1

Step 1: We apply Snell's law at the upper surface of the plate, which gives us: $$n_{a} \sin \theta_{a} = n_{b} \sin \theta_{b}$$ where $n_{a}$ and $n_{b}$ are the refractive indices of air and the plate respectively, and $\theta_{a}$ and $\theta_{b}$ are the Show more…

Show all steps

Thanks for your feedback!

Light is incident in air at an angle $\theta_a$ ($\textbf{Fig. P33.54}$) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. (a) Prove that $\theta_a = \theta'_a$. (b) Show that this is true for any number of different parallel plates. (c) Prove that the lateral displacement $d$ of the emergent beam is given by the relationship $$d = t {\mathrm{sin} (\theta_a - \theta'_b) \over \mathrm{cos} \theta'}$$ where $t$ is the thickness of the plate. (d) A ray of light is incident at an angle of 66.0$^\circ$ on one surface of a glass plate 2.40 cm thick with an index of refraction of 1.80. The medium on either side of the plate is air. Find the lateral displacement between the incident and emergent rays.