This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here's the solution to question 22: I) Complete the table for the values of i and r. | i | r | i | r | | :-------------- | :-------------- | :------- | :------- | | 20^ | 12.7^ | 0.342 | 0.219 | | 30^ | 18.9^ | 0.500 | 0.324 | | 40^ | 25.0^ | 0.643 | 0.423 | | 50^ | 30.0^ | 0.766 | 0.500 | | 60^ | 34.0^ | 0.866 | 0.559 | | 70^ | 37.0^ | 0.940 | 0.602 | II) Draw the graph of i (y-axis) against r (x-axis). Plot the values from the completed table with r on the x-axis and i on the y-axis. The graph should be a straight line passing through the origin. III) Determine the slope of the graph. What does it represent? Step 1: Calculate the ratio ( i)/( r) for each pair of values. This ratio represents the refractive index (n). • For i=20^: (0.342)/(0.219) ≈ 1.562 • For i=30^: (0.500)/(0.324) ≈ 1.543 • For i=40^: (0.643)/(0.423) ≈ 1.520 • For i=50^: (0.766)/(0.500) = 1.532 • For i=60^: (0.866)/(0.559) ≈ 1.549 • For i=70^: (0.940)/(0.602) ≈ 1.561 Step 2: Calculate the average of these ratios to find the slope (refractive index). n = (1.562 + 1.543 + 1.520 + 1.532 + 1.549 + 1.561)/(6) = (9.267)/(6) ≈ 1.5445 The slope of the graph is approximately 1.54. The slope represents the refractive index of the glass. IV) Use the results in b (III) to calculate the velocity of light in glass, given that velocity of light in vacuum is 3.0 × 10^8 m/s. Step 1: Use the formula for refractive index: n = velocity of light in vacuum (c)velocity of light in glass (v_g). n = (c)/(v_g) Step 2: Rearrange the formula to solve for v_g. v_g = (c)/(n) Step 3: Substitute the given values and the calculated refractive index. v_g = 3.0 × 10^8 m/s1.5445 v_g ≈ 1.9423 × 10^8 m/s Rounding to three significant figures: The velocity of light in glass is 1.94 × 10^8 m/s.