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    Refraction, net magnification and internal reflection

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    1. An object of height 2 cm is placed 10 cm in front of a mirror. What type of
    mirror with what radius of curvature is needed to create an upright image with a
    height of 5 cm?

    2. A ray of light strikes the midpoint of one face of an equilateral glass prism
    (n = 1.6) at an angle of incidence of 50°. Trace the path of the ray through the
    glass and find the angles of incidence and refraction at each interface.
    Ignore any dispersion that might take place.

    3. A converging lens of focal length 10 cm is placed 35 cm in front of a concave
    mirror with a radius of curvature of 20 cm. An object is placed 13 cm in front of
    the lens. Locate and describe the final image, and determine its net magnification.
    (ray diagram not required)

    4. A ray of light passes between layers of material as shown. Find the minimum value for θ_2 and the corresponding value of θ_1 that will result in total internal reflection at the glass/air interface.

    See document attached for diagrams.

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    Solution Preview

    See attached file.

    The problems of optics can be best shown with the help of proper ray diagrams. I have answered all the questions in the attached file. So please check for the same.

    Sol: When it is required to get an upright image,(which must be virtual in nature) with a height of 5cm, the magnification can be given by
    Using the similar triangles concept, the magnification of the mirror can be also given by,

    Using this the focal length of the mirror can be calculated from the formula
     f = 50/3 = 16.67 ...

    Solution Summary

    The solution summarizes the steps necessary to solve the questions given.