Geometrical optics

Snell's law

Problem:

A plane wave is propagating from inside material 1 with index of refraction n1 toward a plane interface with material 2, as shown.  The index of refraction of material 2 is n2 = 1.  For angles θi > 50o the wave is totally reflected.
(a)  Find the index of refraction n1 of material 1.
(b)  For θi = 0 find the transmittance T.

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Problem:

A beam of monochromatic light traveling through air strikes the top of a flat slab of glass at an angle 60° to the normal, passes through the glass, and emerges from the bottom of the slab.  The glass has a thickness t and a refractive index n = 1.52.

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(a)  What is the angle of refraction where the light enters the glass?
(b)  Show that the beam emerging from the glass is parallel to the incident beam.

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Problem:

A small source of light is mounted inside a cylindrical container of height h.  The bottom of the container is covered with a mirror.  Initially, the container is empty.  Then a clear liquid with the index of refraction n is slowly poured into the container.  The level of liquid rises steadily, reaching the top of the container in time t.  Find the speed of the image of the source during this process.

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Problem:

A parallel beam of monochromatic light strikes a transparent prism.  The cross section of the prism is a regular hexagon.  The beam is parallel to the “top” and “bottom” faces of the prism, and points A and B in the diagram are the midpoints of the corresponding edges.

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After the refraction, two separate parallel beams of light emerge from the prism. What is the minimum index of refraction of the material of the prism that allows such an effect?

Solution:


Lenses and mirrors

Problem:

A thin lens creates a sharp image of the object onto the wall.  The distance between the object and the wall is nine times the distance from the wall to the closest focal point. What is the object magnification?

Solution:

Problem:

Suppose a certain object with a height of 1 cm is located 10 cm in front of its image, which has a height of 0.5 cm.  Both object and image are upright.  Find the location and focal length of a single thin lens that performs this imaging. 

Solution:

Problem:

An object is placed 8 cm from a thin double convex lens of focal length 12 cm?
(a)  Find the image position and determine whether the image is real or virtual by using the lens formula.
(b)  Repeat part (a) by using graphical construction instead of the lens formula.

Solution:

Problem:

A concave spherical mirror is used by a dentist to produce an enlarged image of a tooth.  If the radius of curvature of the mirror is 2.0 cm, how close is the mirror to the tooth when the image appears triple the size of the tooth?  Is the image erect or inverted?

Solution:

Problem:

Consider optical components centered on the x-axis.
A thin converging lens with focal length f = 2 cm is located at x = 0, and a convex mirror with radius of curvature |R| = 4 cm is located at x = d.
An object is placed at x = -3 cm.  Find the image location and magnification if
(a) d = 10 cm,
(b) d = 5 cm.
Is the image upright or inverted?

Solution:

Problem:

An optical system comprises in turn, from left to right: an observer, a lens of focal length +30 cm, an erect object 20 mm high, and a convex mirror of radius 80 cm. The object is between the lens and the mirror, 20 cm from the lens and 50 cm from the mirror. The observer views the image that is formed first by reflection from the convex mirror and then by refraction from the lens. What is the position of this final image, measured from the mirror, and what is its height?

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