Red light is incident in air on a 30° -60° - 90 ° prism as shown. The incident beam is directed at an angle of ₁ = 47.9⁰with respect to the horizontal and enters the prism at a height h = 27 cm above the base. The beam leaves the prism tothe air at a distance d = 67.5 along the base as shown.52.230⁰1.5961) What is 2, the angle the beam in the prism makes with the horizontal axis?01ddegrees Submit2) What is n, the index of refraction of the prism for red light?12.34485142Your submissions: 52.2 ✓Computed value: 52.2Submitted: Tuesday, November 15 at 11:03 AMFeedback: Your answer has been judged correct; the exact answer is: 52.4776287536106.Submit|h$3Your submissions: 1.596Computed value: 1.596Submitted: Tuesday, November 15 at 11:03 AMFeedback: Your answer has been judged correct; the exact answer is: 1.60120151624339.Your submissions: 12.34485142 X3) What is 3, the angle the transmitted beam makes with the horizontal axis?degrees SubmitG 4) What is 1, max, the maximum value of ₁ for which the incident beam experiences total internal reflection at thehorizontal face of the prism?17.89Your submissions: 17.89 XComputed value: 17.89Feedback:degrees Submitdviolet < d= ddvioletdviolet > dSubmitSubmitted: Tuesday, November 15 at 11:26 AM5) The red beam is now replaced by a violet beam that is incident at the same angle 4₁ and same height h. The prismhas an index of refraction nviolet = 1.71 for violet light. Compare dviolet, the exit distance for violet light, to d, theexit distance for red light.6) Suppose now that the violet beam is incident at height h, but makes an angle ₁,v = 60° with the horizontal. What is93,v, the angle the transmitted beam makes with the horizontal axis?degrees Submit

“Since you have posted a question with multiple sub-parts, we will provide the solution only to the first three sub-parts as per our Q&A guidelines. Please repost the remaining subparts separately.” (1) To find: The angle made by the beam in the prism. Given: The angle ϕ1 is ϕ1=47.9°. The height is h=27 cm. The distance is d=67.5 cm. The prism is shown below.Calculation: The distance c can be obtained as c=htan30=27tan30=46.76 cm The angle ϕ2 can be obtained as ϕ2=tan-1hd-c=tan-12767.5-46.76=52.47° Thus, the angle made by the beam in the prism with the horizontal axis is 52.47°.(2) To find: The index of refraction. Calculation: The angle θ1 and θ2 can be obtained as θ1=90-ϕ1-30=60-47.9=12.1°θ2=180-(90+30+ϕ2)=60-52.47=7.53° The index of refraction can be obtained as n=nosinθ1sinθ2=1×sin12.1sin7.53=1.599≈1.6 Thus, the index of refraction is 1.6.(3) To find: The angle made by the transmitted beam. Calculation: The angle θ can be obtained as θ=90-ϕ2=90-52.47=37.53° The angle θ3 can be obtained as nno=sinθ3sinθ⇒θ3=sin-1nno×sinθ=sin-11.61×sin37.53=77.08° The angle ϕ3 can be obtained as ϕ3=90-θ3=90-77.08=12.92° Thus, the angle made by the transmitted beam with the horizontal is 12.92°.

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Mechanical Engineering

Red light is incident in air on a 30° -60° - 90 ° prism as shown. The incident beam is directed at an angle of ₁ = 47.9⁰ with respect to the horizontal and enters the prism at a height h = 27 cm above the base. The beam leaves the prism to the air at a distance d = 67.5 along the base as shown. 52.2 30⁰ 1) What is 2, the angle the beam in the prism makes with the horizontal axis? 1.596 01 d degrees Submit Your submissions: 52.2 Computed value: 52.2 Submitted: Tuesday, November 15 at 11:03 AM Feedback: Your answer has been judged correct; the exact answer is: 52.4776287536106. 2) What is n, the index of refraction of the prism for red light? 12.34485142 Submit h Your submissions: 1.596 Computed value: 1.596 Submitted: Tuesday, November 15 at 11:03 AM Feedback: Your answer has been judged correct; the exact answer is: 1.60120151624339. 3) What is 3, the angle the transmitted beam makes with the horizontal axis? degrees Submit

Red light is incident in air on a 30° -60° - 90 ° prism as shown. The incident beam is directed at an angle of ₁ = 47.9⁰ with respect to the horizontal and enters the prism at a height h = 27 cm above the base. The beam leaves the prism to the air at a distance d = 67.5 along the base as shown. 52.2 30⁰ 1) What is 2, the angle the beam in the prism makes with the horizontal axis? 1.596 01 d degrees Submit Your submissions: 52.2 Computed value: 52.2 Submitted: Tuesday, November 15 at 11:03 AM Feedback: Your answer has been judged correct; the exact answer is: 52.4776287536106. 2) What is n, the index of refraction of the prism for red light? 12.34485142 Submit h Your submissions: 1.596 Computed value: 1.596 Submitted: Tuesday, November 15 at 11:03 AM Feedback: Your answer has been judged correct; the exact answer is: 1.60120151624339. 3) What is 3, the angle the transmitted beam makes with the horizontal axis? degrees Submit

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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