Geometric Optics
List sign convention for object distance and image distance of mirror/lens
If object is on same side of mirror/lens as incoming ray, then object distance 𝑠 is positive
If image is on same side of mirror/lens as outgoing ray, then image distance 𝑠′ is positive
When does total internal reflection occur?
TIR happens when light goes from a higher refractive index to a lower refractive index. This makes it so there are incident angles where the incident light is completely reflected.
When a charged particle moves through a magnetic field, the direction of the magnetic force on the particle at a certain point A. is in the direction of the magnetic field at that point. B. is opposite to the direction of the magnetic field at that point. C. is perpendicular to the magnetic field at that point. D. depends on the direction of the electric point on that point. E. is none of the above.
C. is perpendicular to the magnetic field at that point.
Electromagnetic induction is a way to convert from some other source of energy to _________ energy (BONUS: give me 2 examples)
electrical
ex: generators, power plants, wireless charging
A diverging lens has a focal length of -15cm. An object is placed 25 cm in front of the lens. What can be said about the image?
A. Real, inverted, and larger than the object
B. Real, inverted, and smaller than the object
C. Virtual, upright, and smaller than the object
D. Virtual, upright, and larger than the object
C. Virtual, upright, and smaller than the object
B of an EM wave at a point in space is 2*10^-6 T. What is the magnitude of Emax of the wave?
E=cB
Emax= 6*10^2 N/C
A positive charge moves straight upward in a region where the magnetic field points out of the page. Which path will the charge follow? a. curve to the left b. curve to the right c. continue straight upward d. curve downward
A. Curve to the left
Based on RHR: v is up, B is out of the page, for a pos. charge force points left. since magnetic force is always perpendicular to velocity, it is circular motion, thus path curves left.
A circular conducting loop lies flat in the plane of the page.A long straight wire is placed to the right of the loop, carrying a current into the page (×).The current in the straight wire is decreasing with time. What is the direction of the induced current in the loop?
A. Clockwise
B. Counterclockwise
C. Zero current
D. Depends on the loop’s radius
E. Depends on the wire’s resistance
A. Clockwise
For straight wire with current into the page, B circles the wire clockwise, thus magnetic field points into the page. Current in wire is decreasing so B into the page is decreasing and the loop wants to oppose the decrease by creating more into the page field. clockwise current produces a magnetic field into the page
A diverging lens has a focal length of 20cm. The lens is thin and in air. You want to place an object so that the lens forms an image that is:, upright, virtual, one half the height of the object. Let the focal length be -20cm, where should I place the object in order to produce this image?
20 cm
at a certain point in space, E and B of an EM wave are given by: E= i(6*10^3)V/m and B= k(2*10^-5)T what direction is this wave propagating in?
E*B= 1.2*10^-1
i*k=-j so E*B= -0.12j, -j= negative y direction
Two long, straight wires are oriented perpendicular to the xy-plane. They carry currents of equal magnitude I in opposite directions as shown. At point P, the magnetic field due to these currents is in A. the positive x-direction. B. the negative x-direction. C. the positive y-direction. D. the negative y-direction. E. none of the above
A. the positive x-direction
For a long straight wire with current along +z (out of page), the magnetic field circles counterclockwise.
A square conducting loop lies in the plane of the page.
A long straight wire is placed above the loop, carrying a current I to the right.The current in the straight wire begins to decrease steadily. What is the direction of the induced current in the loop?a. Clockwise
b. Counterclockwise
c. Zero current
d. Depends on the loop’s resistance
A. Clockwise
current to the right means that magnetic field is into the page. current decreasing means loop wants to oppose the decrease by increasing more into the page field, thus direction is clockwise
An object is placed beyond the center of curvature of a concave mirror. Which of the following correctly describes the image formed, based on principal‑ray construction?
A. Virtual, upright, and larger than the object
B. Real, inverted, and larger than the object
C. Real, inverted, and smaller than the object
D. Virtual, inverted, and smaller than the object
C. Real, inverted, and smaller than the object
A beam of light in air strikes a flat slab of acrylic (index n=1.49) at an angle of incidence of 35 degrees. The acrylic slab is in contact with a layer of water (index n=1.33 ) on the opposite side.a. calculate the angle of refraction inside the acrylic b. the light then passes from acrylic into water, compute the angle of refraction in the water
a. 22.6 degrees
b. 25.5 degrees
A particle with charge +2c moves with velocity= ( 1i -2j +3k)m/s. It is in a region where the electric and magnetic fields are E= (4i+1j-2k)V/m and B= (01+3j+1k)T, Compute the total lorentz force on the particle.
F= -14i, 0j, 2k N
A circular conducting loop of radius R lies in the plane of the page. A uniform magnetic field B= B_0*k points out of the page and is constant in time. A mechanical device pulls on the loop so that its radius increases at a constant rate of dR/dt=v. What is the magnitude and direction of the induced emf?
E= 2pi * R* B_0 *v, clockwise
A concave mirror has a focal length of 20cm, an object 5cm tall is placed 30cm in front of the mirror. a. Using principal rays, describe qualitatively where the image forms (relative to F and C) and whether it is real or virtual, upright or inverted, magnified or reduced. b. compute image distance c. compute magnification
a. s= 30cm is between 20cm and 40cm, for a concave mirror an object bw F and C produces an image that is real, inverted, magnified, located beyond C. this matches the standard principal ray diagram: ray parallel to the axis reflects through F, ray through C reflects back on itself, ray through F reflects parallel to the axis, all 3 rays intersect beyond c
b. s'= 60cm
c. magnification= -2
A ray of light travels inside a glass block with refractive index n=1.6. It approaches the glass–air boundary at an angle of incidence theta_i .
a. Compute the critical angle for the glass–air interface. b.If the ray strikes the boundary at 50 degrees , determine whether total internal reflection occurs.
a. 38.7 degrees
b. TIR does occur
A particle with charge -3C moves with velocity (2i -j +4k) m/s. It enters a region where B is (-3i+2j+k)T. What is the direction of the magnetic force?
A. Mostly in the +x direction, with smaller +z component
B. Mostly in the −x direction, with smaller −y component
C. Mostly in the +y direction, with smaller −z component
D. Mostly in the −y direction, with smaller +x component
C. Mostly in the +y direction, with smaller −z component
Compute cross product: v*B= -9i -14j +k * -3C = F = 27i +42j -3k
Largest component is y, then x, then -z so the force points mostly in y with a small -z tilt.
There is a uniform time independent magnetic field B pointing into the page. A slide wire is moving to the right with constant velocity v. Find the direction and magnitude of the emf in the rectangular loop as a function of B, v, L
E= B*L*v, CCW
v is to the R, B is into the page, v*B points upward along the sliding wire, so pos. charges are driving upward into the moving rod giving an induced CCW current around the loop