Solve the problems by showing all the steps.

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1.) Image Formation by Mirrors:

An object is placed at a distance of 100 cm in front of a convex mirror. A plane mirror is placed at a distance of 40 cm from the convex mirror on the same side as the object. Find the focal length of the convex mirror if the images formed by the two mirrors coincide.

2.) Total Internal Reflection:

The critical angle of incidence in a glass slab immersed in air is 30^o. What will be the critical angle when it is immersed in a medium of refractive index2?

3.) Image Formation by Lenses:

A camera with a 55.0 mm focal length lens is being used to photograph a person standing 3.50 m away.

1. How far from the lens must the film be?
2. If the film is 36.0 mm high, what fraction of a 1.70 m tall person will fit on it?

4.) Refractive Index:

Components of some computers communicate with each other through optical fibers having an index of refraction n=1.55. What time in nanoseconds is required for a signal to travel 0.25 m through such a fiber?

5.) Image Formation by Mirrors:

1. Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature.
2. What is its power in diopters?