How deep does a point in the middle of the

Question

1. A single concave spherical mirror is used to create an image of a source 6.80 cm tall that is located at position x = 0 cm which is x_o = 18.0 cm to the left of Point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature for the mirror is R = 13.5 cm. Calculate the position x_i where the image is formed. Use the coordinate system given in the drawing. What is the height h_i of the image? Is the image upright or inverted (upright = pointing up, inverted = pointing down)? Is it real or virtual? Ans:- 22.9 cm, 1.85 cm, inverted, real

 

 

•        2.  A ray of light is incident on an equilateral triangular prism with an index of refraction of 1.29. The ray is parallel to the base of the prism when it approaches the prism. The ray enters the prism at the midpoint of one of its sides, as shown in the figure. What is the direction of the ray when it emerges from the triangular prism? Ans:- 21.2 degree

•         3. In a step-index fiber, the index of refraction undergoes a discontinuity (jump) at the core-cladding interface, as shown in the figure. Infrared light with wavelength 1530 nm propagates through such a step-index fiber through total internal reflection at the core-cladding interface. The index of refraction for the core at 1530 nm is  n_core = 1.48. If the maximum angle α_max at which light can be coupled into the fiber such that no light will leak into the cladding is  α_max = 13.832°, calculate the percent difference between the index of refraction of the core and the index of refraction of the cladding. (Let d_core = 9 µm and d_cladding = 125 µm.) Ans:- 1.31. %

•         Refer to the figure below and prove that the arc of the primary rainbow represents the 42° angle from the direction of the sunlight.

•         4. A concave mirror forms a real image twice as large as the object. The object is then moved such that the new real image produced is three times the size of the object. If the image was moved 69.0 cm from its initial position, how far was the object moved? What is the focal length of the mirror? Ans:- 11.5 cn, 69 cm

 

•         How deep does a point in the middle of the floor of a 3-m-deep pool appear to a person standing 3.3 meters horizontally from the point? Take the refractive index for the pool to be 1.3 and for air to be 1. (Assume the person is standing in the pool with their eyes just above the level of the water.) Ans:-0.938 m