Homework #6
Due Nov. 26th AM 09:30
Problem 1
A triangular glass (n = 1.50) prism with an angle is
depicted. What is the smallest angle of incidence ( ) for
which the light ray can emerge from the other side?
Problem 2
A coin lies at the bottom of a pool of liquid (n) and depth d. As observer uses both her eyes, the
observer will perceive the coin to at depth da ( < d). Show that
.
Problem 3
A glass sphere has radius R and index of refraction ng. A paperweight is
constructed by slicing through the sphere so that it is left with height h as
shown in the figure. The paperweight is placed on a table and viewed from
directly above by an observer who is distance d from the tabletop. When
viewed through the paperweight glass, the tabletop may appear to be at a
distance do to the observer. Find an expression of the distance do in terms
of R, ng, h, and d.
Problem 3
Consider a tip of an endoscope depicted. The
spherical end (n = 1.50) is attached to an optical
fiber bundle (r = 1.00 mm < R) so that its center
aligns with the central axis of the fiber. Consider
laser light that travels precisely parallel to the
central axis of the fiber and then refracts out from
the surface of the sphere into air. (a) If the laser light, traveling along the edge of the fiber, refracts out
of the sphere tangent to the surface of the sphere, what is the radius of the sphere? (b) For such a light,
what is the angle by which the direction changes as it leaves the sphere (angle of deviation)? (c) Show
that the light traveling along the edge of the fiber will have the largest angle of deviation.
Problem 4
Consider the following arrangement. A thin converging
lens (with radii of curvatures R1 = 9.00 cm and R2 = 11.0 cm) is in front of a concave spherical mirror with R
= 8.00 cm. If the focal points for the lens are F1 and F2 (= 5.00 cm from the center of the lens), (a)
what is the index of refraction of the lens material? (b) If the lens and the mirror are distance D apart
and an object is placed distance d left of the lens, what is the position of the final image and the
magnification as seen by the eye? (c) Is the final image inverted or upright?
Problem 5
Consider two parabolic mirrors with focal length (f = 7.50 cm) facing each
other so that their centers are f apart. If an object is placed at the bottom mirror,
an image of the object is formed at a small opening at the center of the top
mirror. Show that the final image is formed at such location and describe its
characteristics.
Problem 6
Two microscopic slides touch at one end and are separated at the other
end. When light of shines vertically, an overhead observer sees an
interference pattern on the slides with dark fringes separated by s.
Express the angle between the slides.
Problem 7
Two wavelengths and
(with
) are incident normally on a diffraction grating. Show
that the angular separation between spectral lines in the mth-order spectrum is:
where d is the slit spacing and m is the order number.
Problem 8
Derive the following expression for the intensity pattern for a three-slit ‘grating’ (
).
and
Problem 9
For a more general case of constructive interference by reflection from a thin film where the incident
light on the film makes a non-zero angle (relative to the normal), show that the condition for
constructive interference is
where n is the index of refraction, t the thickness,
and is the angle of refraction.
Problem 10
A soap film (n = 1.33) is contained within a rectangular wire frame held vertically. The film drains
downward so that thickness at the top is nearly zero. A reflected white light with near normal
incidence is used to view the film, and the first violet (
nm) interference band is observed 3.0
cm from the top edge of the film. (a) Where from the top is the red (
nm) interference band?
(b) What are the thicknesses of the soap film at violet and red bands?