Optics Practice Problems

  1. Which of the following is the correct formula for focal point calculation?
  1. \(F=I+O\)
  2. \(\frac{1}{F}=I\times \frac{1}{O}\)
  3. \(F=1\times \frac{1}{O}\)
  4. \(\frac{1}{F}=\frac{1}{I}+\frac{1}{O}\)
Show Answer
The correct answer is D!

The thin‐lens equation relates focal length \(F\), image distance I, and object distance O by:

\(\dfrac{1}{F}=\dfrac{1}{I}+\dfrac{1}{O}\)

This reciprocal form holds for both converging and diverging lenses.

 

  1. Which of the following is the correct formula for lens power?
  1. \(P = \frac{1}{f} + \frac{1}{O}\)
  2. \(P = \frac{1}{f}\)
  3. \(P=f\times0\)
  4. \(P=\frac{O}{f}\)
Show Answer
The correct answer is B!

Lens power \(P\), in diopters, is defined as the reciprocal of the focal length (in meters):

\(P=\dfrac{1}{f}\)

Choices A, C, and D introduce extra terms or multiply by zero, so Choice B matches the definition.

 

  1. The absolute index of refraction for a substance is 2.0 for light having a wavelength of \(5.9 \times 10^{-7}\) meters. In this substance what is the critical angle for light incident on a boundary with air?
  1. 25°
  2. 30°
  3. 35°
  4. 40°
Show Answer
The correct answer is B!

Total internal reflection at the critical angle \(θ_c\) satisfies the following:

\(\sin\theta_c=\dfrac{n_2}{n_1}\)

Here, \(n_1=2.0\) and \(n_2\approx1.0\), so:

\(\sin\theta_c=\dfrac{1}{2}=0.5\)

This gives \(θ_c=30°\).

 

  1. Which phenomenon can occur with light but not with sound?
  1. Doppler effect
  2. Interference
  3. Polarization
  4. Refraction
Show Answer
The correct answer is C!

Polarization requires transverse oscillations perpendicular to propagation. Light is a transverse wave and can be polarized; sound in air is longitudinal and cannot.

 

  1. The threshold frequency of a photo emissive surface is \(7.0 \times 10^{14} \text{ hz}\). Which electromagnetic radiation, incident upon the surface, will produce the greatest amount of current?
  1. Low intensity infrared radiation
  2. High intensity infrared radiation
  3. Low intensity UV radiation
  4. High intensity UV radiation
Show Answer
The correct answer is D!

Only photons with frequency ≥ the threshold can eject electrons. Infrared is below threshold and produces no current, regardless of intensity.

UV above threshold will, and higher intensity (more photons) yields greater current.

 

  1. A spherical mirror that forms only virtual images has a radius of curvature of 0.5 meters. What is the focal length of this mirror?
  1. -0.125 m
  2. -0.25 m
  3. 2.5 m
  4. 2.75 m
Show Answer
The correct answer is B!

For spherical mirrors, \(f=\tfrac{R}{2}\). A mirror forming only virtual images is convex (negative focal length).

\(R=0.50 \text{m}\)

\(f=\:–0.25 \text{m}\)

 

  1. A spherical concave mirror is used in the back of a car headlight. Where must the bulb of the headlight be located to produce a parallel beam of reflected light?
  1. Between the principal focus and the mirror
  2. Beyond the center of curvature of the mirror
  3. At the principal focus of the mirror
  4. At the center of the curvature of the mirror
Show Answer
The correct answer is C!

A concave (converging) mirror will reflect rays from its focal point into a parallel beam. Place the bulb at the principal focus and the reflected light becomes collimated.

 

  1. An object 0.080 meters high is placed 0.20 meters from a converging (convex) lens. If the distance from the image of the lens is 0.40 meters, what is the height of the image?
  1. 0.08 m
  2. 0.16 m
  3. 0.24 m
  4. 0.33 m
Show Answer
The correct answer is B!

Magnification is \(m=–\dfrac{v}{u}\), where \(u=0.20 \text{m}\) and \(v=0.40 \text{m}\).

So \(m=\:–2\) and image height is \(–2\times0.080 \text{m}=\:–0.16 \text{m}\) (0.16 m in magnitude, inverted).

 

  1. A diverging (concave) lens can form images that are…
  1. Virtual only
  2. Inverted only
  3. Either virtual or real
  4. Either inverted or erect
Show Answer
The correct answer is A!

A diverging lens always produces virtual, upright, reduced images for real objects. It cannot form a real image because rays diverge after passing through.

 

  1. A ray of light strikes a plane mirror at an angle of incidence equal to 35°. What is the angle between the incidence ray and the reflected ray?
  1. 45°
  2. 60°
  3. 70°
  4. 80°
Show Answer
The correct answer is C!

The law of reflection gives equal angles of incidence and reflection (35° each), so the two rays form a \(35°+35°=70°\) angle between them.

 

  1. Compared to the wavelengths of visible light, the wavelengths of UV light are…
  1. Shorter
  2. Longer
  3. The same
Show Answer
The correct answer is A!

UV light has higher frequency (and therefore shorter wavelength) than visible light since \(c=\lambda\nu\).

 

  1. What is the energy of a quantum of light having a frequency of \(6.0 \times 10^{14} \text{ Hz}\) ?
  1. \(1.6 \times 10^{−4}\text{ J}\)
  2. \(4.0 \times 10^{−19}\text{ J}\)
  3. \(1.3 \times 10^{−11}\text{ J}\)
  4. \(5.0 \times 10^{-7}\text{ J}\)
Show Answer
The correct answer is B!

Photon energy is \(E=h\nu\).

\(h\approx 6.63\times 10^{−34}\text{ J}\cdot \text{s}\)

\(\nu=6.0\times10^{14}\text{ Hz}\)

\(E\approx3.98\times10^{−19}\text{ J}\)

This rounds to \(4.0\times10^{−19}\text{ J}\).

 

  1. Experiments performed with light indicate that light exhibits which properties?
  1. Particle properties only
  2. Wave properties only
  3. Both particle and wave properties
  4. Neither particle nor wave properties
Show Answer
The correct answer is C!

Light shows wave phenomena and particle phenomena, so it has both natures.

 

  1. What is the speed of light in a medium having an absolute index of refraction of 2.3?
  1. \(0.77 \times 10^7\text{ m/s}\)
  2. \(1.3 \times 10^8\text{ m/s}\)
  3. \(1.5 \times 10^3\text{ m/s}\)
  4. \(2.3 \times 10^8\text{ m/s}\)
Show Answer
The correct answer is B!

Speed in a medium is \(v=\dfrac{c}{n}\).

\(c=3\times10^8 \text{m/s}\)

\(n=2.3\)

\(v\approx 1.30\times 10^8 \text{m/s}\)