Calculate Index of Refraction: Air to Glass

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The index of refraction from air to glass is calculated using the formula n2 = n1 * sin(theta1) / sin(theta2). With n1 as 1 for air, sin(theta1) at 30 degrees, and sin(theta2) at 20 degrees, the result is n2 = 1.46. This indicates that light travels approximately 1.46 times slower in glass than in air. The difference in the index of refraction is attributed to the varying densities and optical properties of the two materials. Understanding this concept is crucial for analyzing light behavior during refraction and total internal reflection.
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In this figure the path of the light passes from air to glass. Calculate the index of refraction
n1 = air = 1
n2 = glass = ?
Sin theta 1 = 30degrees
sin theat 2 is = 20 degrees

formula used n2 = n1*sin theta 1 / sin theta 2

sin of 30/ sin of 20 = n2 = 1.46 is this correct
hope the attachment went through will have to see before making judgement
 

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Yes, your calculation is correct. The index of refraction from air to glass is 1.46. This means that light travels approximately 1.46 times slower in glass compared to air. This is due to the different density and optical properties of air and glass. The index of refraction is an important factor in determining the behavior of light as it passes through different materials, and is essential in understanding phenomena such as refraction and total internal reflection.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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