OAT Physics: Optics and Waves Questions and Answers — Questions and Answers
Question 1: A beam of monochromatic light travels from water (n ≈ 1.33) into an unknown transparent medium. If the angle of incidence in the water is 30° and the angle of refraction in the new medium is 22°, what is the index of refraction of the unknown medium?
- 1.00
- 1.33
- 1.52
- 1.80 (Correct answer)
Correct answer: 1.80
This problem is solved using Snell's Law, which relates the indices of refraction and the angles of incidence and refraction for light passing between two media. The formula is n₁sin(θ₁) = n₂sin(θ₂). Here, n₁ = 1.33 (water), θ₁ = 30°, and θ₂ = 22°. We need to solve for n₂. Rearranging the formula gives n₂ = n₁(sin(θ₁)/sin(θ₂)). Plugging in the values: n₂ = 1.33 * (sin(30°)/sin(22°)) = 1.33 * (0.5 / 0.3746) ≈ 1.775, which rounds to 1.80.
Question 2: An object is placed 40 cm in front of a converging lens, which forms a real, inverted image 60 cm on the other side of the lens. What is the focal length of this lens?
- 12 cm
- 24 cm (Correct answer)
- 50 cm
- 100 cm
Correct answer: 24 cm
The relationship between object distance (dₒ), image distance (dᵢ), and focal length (f) for a thin lens is given by the thin lens equation: 1/f = 1/dₒ + 1/dᵢ. For a converging lens forming a real image, both dₒ and dᵢ are positive. Given dₒ = 40 cm and dᵢ = 60 cm, we can calculate f: 1/f = 1/40 + 1/60. To add these fractions, find a common denominator, which is 120. So, 1/f = 3/120 + 2/120 = 5/120. Therefore, f = 120/5 = 24 cm.
Question 3: Which of the following changes will increase the angular separation (θ) between the central maximum (m=0) and the first-order maximum (m=1) in a diffraction grating experiment?
- Decreasing the wavelength of the light used.
- Increasing the distance between the grating and the screen.
- Using a grating with more lines per millimeter. (Correct answer)
- Decreasing the intensity of the light source.
Correct answer: Using a grating with more lines per millimeter.
The condition for constructive interference for a diffraction grating is given by the equation d sin(θ) = mλ, where d is the slit separation, θ is the angular separation, m is the order of the maximum, and λ is the wavelength. To increase θ, sin(θ) must increase. Rearranging for sin(θ) gives sin(θ) = mλ/d. Increasing θ can be achieved by increasing the wavelength (λ) or decreasing the slit separation (d). Using a grating with more lines per millimeter means the distance 'd' between each line is smaller. A smaller 'd' in the denominator leads to a larger value for sin(θ), and thus a larger angle θ.
Question 4: A stationary observer hears a fire truck's siren. As the fire truck moves away from the observer at a constant speed, which of the following properties of the sound wave perceived by the observer decreases?
- Wavelength
- Speed of the wave
- Frequency (Correct answer)
- Amplitude
Correct answer: Frequency
This scenario describes the Doppler effect for sound. When a sound source moves away from a stationary observer, the wave crests reach the observer less often than if the source were stationary. This results in the observer perceiving a lower frequency (lower pitch). The speed of the sound wave in the medium (air) remains constant, determined by the properties of the air itself. The wavelength increases as the source moves away. While the amplitude (loudness) would also decrease due to the increasing distance, the defining characteristic of the Doppler effect in this situation is the decrease in frequency.
Question 5: Which of the following statements is true for all types of electromagnetic waves, including radio waves, visible light, and X-rays, when traveling in a vacuum?
- They all have the same frequency.
- They all have the same wavelength.
- They all have the same speed. (Correct answer)
- They all carry the same amount of energy per photon.
Correct answer: They all have the same speed.
A fundamental principle of electromagnetism is that all electromagnetic waves propagate through a vacuum at the same constant speed, known as the speed of light (c), which is approximately 3.0 x 10⁸ m/s. Electromagnetic waves have a wide spectrum of frequencies and corresponding wavelengths, which are inversely related (c = fλ). The energy of a photon is directly proportional to its frequency (E = hf), so different types of EM waves have different photon energies.
Question 6: Unpolarized light with an initial intensity of I₀ is incident on an ideal polarizing filter. What is the intensity of the light that passes through the filter?
- I₀
- I₀ / √2
- I₀ / 2 (Correct answer)
- 0
Correct answer: I₀ / 2
Unpolarized light consists of electric field oscillations in all random directions perpendicular to the direction of propagation. An ideal polarizer only allows the component of the electric field that is aligned with its transmission axis to pass through. On average, this component corresponds to half of the total intensity of the unpolarized light. Therefore, the intensity of the transmitted light is I₀ / 2.
OAT Physics: Optics and Waves Questions and Answers
A beam of monochromatic light travels from water (n ≈ 1.33) into an unknown transparent medium.
If the angle of incidence in the water is 30° and the angle of refraction in the new medium is 22°, what is the index of refraction of the unknown medium?