šŸŒŠ Unit 4: Wave Nature of Light ā€” Practice Quiz

Assessment AS Learning
šŸ”„ Not Graded ā€” Unlimited Retakes
Purpose: Self-check understanding after each topic. Use results to plan study before the unit test. Use \(c=3.00\times10^8\,\text{m/s}\), \(h=6.63\times10^{-34}\,\text{JĀ·s}\).

šŸ“‹ Formulae

\(c=f\lambda\) | \(n_1\sin\theta_1=n_2\sin\theta_2\) | \(\sin\theta_c=n_2/n_1\) | \(d\sin\theta=m\lambda\) | \(\Delta y=\lambda L/d\) | \(a\sin\theta=m\lambda\) (single-slit min) | Thin film (low-high-low): \(2nt=(m+\tfrac12)\lambda\) | \(I=I_0\cos^2\theta\)
Score: 0 / 9
Q1 ā€” Frequency from wavelength
A laser emits red light of wavelength \(632.8\,\text{nm}\) in vacuum. Calculate its frequency in \(10^{14}\,\text{Hz}\).
Answer: Ɨ10Ā¹ā“ Hz
Solution:
\(f = c/\lambda = 3.00\times10^8/632.8\times10^{-9} = 4.74\times10^{14}\,\text{Hz}\).
Q2 ā€” Refraction (Snell's law)
Light passes from air (\(n=1.00\)) into glass (\(n=1.50\)) at \(\theta_1=35Ā°\). Find the angle of refraction (degrees).
Answer: Ā°
Solution:
\(\sin\theta_2 = (1.00/1.50)\sin 35Ā° = 0.382 \Rightarrow \theta_2 = 22.5Ā°\).
Q3 ā€” Critical angle
Calculate the critical angle for light going from water (\(n=1.33\)) into air. Answer in degrees.
Answer: Ā°
Solution:
\(\sin\theta_c = 1/1.33 \Rightarrow \theta_c = 48.8Ā°\).
Q4 ā€” Young's double slit
Slits \(0.15\,\text{mm}\) apart are illuminated by \(\lambda=600\,\text{nm}\) light. The screen is \(2.0\,\text{m}\) away. Find the fringe spacing in mm.
Answer: mm
Solution:
\(\Delta y = \lambda L/d = (6\times10^{-7})(2)/(1.5\times10^{-4}) = 8.0\times10^{-3}\,\text{m}=8.0\,\text{mm}\).
Q5 ā€” Diffraction grating
A grating with 4000 lines/cm produces a 1st-order maximum at \(\theta=14Ā°\). Find the wavelength (nm).
Answer: nm
Solution:
\(d = 1/4000\,\text{cm}=2.5\times10^{-6}\,\text{m}\). \(\lambda = d\sin\theta = 2.5e{-}6 \times \sin 14Ā° = 6.05\times10^{-7}\,\text{m}=605\,\text{nm}\).
Q6 ā€” Single-slit diffraction
Light of \(\lambda=500\,\text{nm}\) passes through a slit of width \(0.10\,\text{mm}\). Find the angular position (degrees) of the first minimum.
Answer: Ā°
Solution:
\(\sin\theta = \lambda/a = 5\times10^{-7}/10^{-4}=5\times10^{-3}\Rightarrow\theta\approx 0.286Ā°\).
Q7 ā€” Polarization (Malus)
Unpolarized light of intensity \(I_0\) passes through one polarizer, then a second polarizer at \(60Ā°\) to the first. Express transmitted intensity as a fraction of \(I_0\).
Solution:
After 1st: \(I_0/2\). After 2nd: \(I_0/2 \cdot \cos^2 60Ā° = I_0/2 \cdot 1/4 = I_0/8\).
Q8 ā€” Wave-particle conceptual
Which observation cannot be explained by a pure wave model of light?
Solution:
The photoelectric threshold (no emission below a critical \(f\) regardless of intensity) requires the photon model.
Q9 ā€” Thin film
A thin oil film (\(n=1.40\)) on water (\(n=1.33\)) appears to reflect green light (\(\lambda=550\,\text{nm}\)) strongly. Find the minimum non-zero film thickness (nm). Use the constructive condition appropriate for low-high-low: \(2nt=(m+\tfrac12)\lambda\).
Answer: nm
Solution:
\(t_{min}=\lambda/(4n)=550/(4\cdot1.40)=98.2\,\text{nm}\).

šŸ“Š Self-Reflection

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