Math Problem Statement

বায়ু সাতে কোনো মাধ্যমের প্রতিসরাঙ্ক √2। বায়ুতে আলোক রশির আপতন কোণ 45° হলে প্রতিসরণের ক্ষেত্রে ওই রশির চ্যুতি কোন হবে নির্ণয় করো।

Solution

The question is written in Bengali and asks to determine the angle of deviation of a light ray when it passes from air into a medium with a refractive index of 2\sqrt{2}, given that the angle of incidence is 4545^\circ.

Let's solve this step by step:

Given Data:

  • Refractive index of the medium: n=2n = \sqrt{2}
  • Angle of incidence: i=45i = 45^\circ
  • Using Snell's Law:
    n1sini=n2sinrn_1 \sin i = n_2 \sin r Since the light is traveling from air (n1=1n_1 = 1) into the medium (n2=2n_2 = \sqrt{2}), we get: 1×sin45=2×sinr1 \times \sin 45^\circ = \sqrt{2} \times \sin r Since sin45=12\sin 45^\circ = \frac{1}{\sqrt{2}}, the equation becomes: 12=2sinr\frac{1}{\sqrt{2}} = \sqrt{2} \sin r sinr=12×2=12\sin r = \frac{1}{\sqrt{2} \times \sqrt{2}} = \frac{1}{2} r=sin1(0.5)=30r = \sin^{-1} (0.5) = 30^\circ

Step 2: Finding the Angle of Deviation

The deviation angle DD is given by: D=irD = i - r D=4530=15D = 45^\circ - 30^\circ = 15^\circ

Final Answer:

The angle of deviation is 1515^\circ.

Would you like a more detailed explanation? Here are some related questions to explore further:

  1. What happens to the deviation angle if the refractive index increases?
  2. How is the refractive index related to the speed of light in a medium?
  3. What would be the deviation angle if the light was traveling from the medium into the air?
  4. Can total internal reflection occur in this case? Why or why not?
  5. How does Snell's Law apply in cases of multiple refractions?

Tip: Always remember that refraction bends light towards the normal when entering a denser medium and away from the normal when entering a less dense medium.

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Math Problem Analysis

Mathematical Concepts

Snell's Law
Trigonometry
Angle of Deviation

Formulas

Snell's Law: n1 * sin(i) = n2 * sin(r)
Angle of Deviation: D = i - r

Theorems

Snell's Law

Suitable Grade Level

Grades 9-10