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Final Exam
Physics 2220
Name:
Adam Payne (JFB 102)
Summer 2014
Circle your Discussion TA:
Friday 1 August
Mei Hui Teh (LCB 215)
Chris Winterowd (LCB 225)
You may use your four sheets of notes and formulas, but you must not collaborate with any
other person. Do all four problems, showing your method and working clearly (a correct answer
alone is not necessarily sufficient). Be sure to include correct SI units in your answers where
appropriate. The number of marks for each part is given in square brackets, [ ], to its right.
1. (a) Two conducting spheres are connected to each other by a thin, straight, flexible
conducting wire in such a way that the centres of the two spheres are distance 12R apart. The
radius of sphere 1 is R, and the radius of sphere 2 is 2R, Together, the spheres carry a total
charge 6Q. Assume that the spheres are far enough apart that charge is distributed uniformly
over the surface of each. Using subscripts 1 and 2 as needed, find each of the following in terms
of Q, R, and fundamental constants such as ke, e 0i and n:
(i) the charges, qi and qa, on the spheres;
[6]
(ii) the surface charge densities,CTIand aa, of the spheres;
[4]
(The surface area of a sphere of radius r is 4:rr2.)
(iii) the electric field magnitudes, EI and £2, at the surfaces of the spheres;
(iv) the tension in the connecting wire.
[2]
(b) A parallel-plate capacitor has circular plates of radius R and
plate separation d. When the current in the wire connected to
the capacitor is I, use the Maxwell-Ampere law to derive an
expression for the magnitude, B, of the magnetic field between
the plates of the capacitor at distance 3/4R from its axis.
[8]
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Physics 2220, Summer 2014
Name:
Final Exam
Circle TA:
Adam
Chris
2. Consider a pure, transparent block of ice
(refractive index 1.309) lying on a horizontal
table. The block is in the shape of a cube of
length 8,00 cm along each edge.
Looking down from above, we see a
horizontal ray of light enter the block at the
centre of the left-hand face (angle of incidence
9). The refracted ray undergoes total internal
reflection at the top face of the cube and
eventually emerges into the air from the righthand face (angle of refraction <))), as shown in
the sketch (not drawn to scale) at the right.
(a) If 9 = 50.0 °, find the value of <j) [3] and the angle of deviation, 5 (i.e., the angle
between the incident and emergent rays of light). [3]
(b) What are the largest [8] and smallest [8] values 9 can have such that total internal
reflection still occurs inside the cube at the top face?
(c) Qualitatively, how would the answers to part (b) be affected if the block of ice were
immersed in ethyl alcohol (n = 1.361) instead of air? [2]
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Physics 2220, Summer 2014
Name :
Final Exam
Circle TA :
Adam
Mei
Chris
3, (a) When light travelling in transparent medium 1 is incident upon the interface between it
and transparent medium 2, the polarizing angle '(that is, Brewster's angle) is found to be 48.0°.
Explain as precisely as you can the circumstances under which light encountering the interface
between media 1 and 2 would experience total internal reflection. (Specify both the direction of
travel of the light and its angle of incidence.)
[8]
(b) A lens is made of glass of refractive index 1.50. The front spherical surface of the lens
has its centre of curvature 12.0 cm behind the lens. When parallel rays of light in air are shone on
to this lens along the direction of its axis, they are brought to focus 20.0 cm behind the lens.
(i) Where is the centre of curvature for the back spherical surface of the lens?
[6]
(ii) When the lens is immersed in a transparent liquid, parallel rays of light are brought to
focus 1 1 5 cm behind the lens. What is the index of refraction of the liquid?
[6]
(c) An object of height 1.6 cm stands on the axis of a concave (converging) spherical mirror
whose radius of curvature is 20 cm. The image formed by the mirror is upright and is 8.0 cm tall.
Where are the object and the image located in relation to the mirror ?
[8]
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Physics 2220, Summer 2014
Name:
Final Exam
Circle TA :
Adam
Mei
Chris
4. (a) When a Young's double slit experiment is performed with two slits (each having width a)
separated by centre-to-centre distance d, it is noticed that 11 bright interference fringes appear
within the central diffraction maximum.
(i)
Find d as a multiple of a.
[4]
(ii) Taking diffraction effects into account, how intense is the m = 4 interference
maximum compared with the intensity of the central maximum? Give your answer
correct to the nearest whole per cent.
[8]
(b) A thin, transparent coating of material of refractive index 1 .40 is to be applied to a glass
camera lens of refractive index 1.50, in order to inhibit (by means of destructive interference)
reflection of light in the middle of the visible spectrum (wavelength 550 nm). What is the
minimum thickness needed for such a coating?
[8]
(c) Suppose that you want to reduce the intensity of vertically polarized light by 22 per cent.
You are going to achieve this reduction in intensity by passing the light through a polarizing sheet
(after which it will no longer be polarized in the vertical plane). To the nearest degree, what angle
should the transmission axis of the polarizing sheet make with the vertical?
[4]
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4. (cont'd)
Name: