A glass sphere 30cm in radius is used to bring sunlight to a focus. Using principal points, determine the location of focus point relative to the back vertex of the sphere? Redo the calculation using the matrix approach, and show that you get the same answer. Let the index of refraction of the glass be 1.4.

(a) An opaque cylindrical tank with an open top has a diameter of 2.60 m and is completely filled with water. When the afternoon sun reaches an angle of 31.5° above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank (in m)? 4 Determine how the depth of the tank is related to the angle of refraction for the geometry described in the question. Drawing a diagram may be helpful. Then apply Snell's law to find the angle of refraction and use it to determine the depth of the water in the tank. m (b) What If? On winter solstice in Seattle, the sun reaches a maximum altitude of 19° above the horizon. What would the depth of the tank have to be (in m) for the sun not to illuminate the bottom of the tank on that day? m

Example 7: During the investigation of a new type of optical fiber having an index of refraction n = 1.21, a laser beam is aimed at the flat end of a straight fiber, as shown in the figure. What is the maximum angle of incidence 01 if the beam is not to escape from the sides of the fiber if it is surrounded by air?

A very large piece of clear ice has a cave man frozen inside it. When viewed at an anglefrom the top of the ice the cave man appears to be 1.00 ft below the surface of the ice.What is the actual depth (in units of inches) of the cave man from the top of the ice?The index of refraction of the ice is 1.309   Do NOT use i for the angle of incidence or r for the refracted angle

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 51.0° when submerged in carbon tetrachloride, which has an index of refraction of 1.461? (b) What would the critical angle be for this substance in air?

As shown below light reflects off the horizontal surface before striking the vertical surface at the critical angle theta equals 27° the speed of light and material B is 2.86×10^8 m/s. determine theta i and the index of refraction in material A

A beam of light is incident on a square piece of glass with side s =  10.0 cm and index of refraction 1.50. The angles are shown in the figure to scale (you can count the blocks to measure them if you don't have a protractor). Where does the beam exit the glass? Assume the glass is in air (n = 1.00).