Lesson: Light – A-Level Physics Exam Preparation
Hello everyone! Welcome to this comprehensive summary of the "Light" chapter, which is one of the most frequently tested topics in A-Level Physics under the "Mechanical Waves and Light" section. This topic connects visual intuition directly to mathematical models, covering both geometric optics and wave optics.
Let’s walk through the essential principles step by step, following the official exam blueprint.
---1. Reflection and Mirrors
When light strikes a boundary between two media, a portion of the light bounces back into the original medium. This is governed by the Law of Reflection:
- The incident ray, the reflected ray, and the normal to the surface all lie in the same plane.
- The angle of incidence equals the angle of reflection: \( \theta_i = \theta_r \) (measured relative to the normal line).
Plane Mirrors
A plane mirror forms an image with the following characteristics:
- The image is virtual, upright, and laterally inverted (swapped left-to-right).
- The image distance equals the object distance: \( s' = s \).
- The image size equals the object size: \( y' = y \) (magnification \( m = 1 \)).
Spherical Mirrors (Concave and Convex)
Spherical mirrors are curved reflective surfaces with a radius of curvature \( R \). The focal length is given by:
\( f = \frac{R}{2} \)
Mirror Equation:
\( \frac{1}{f} = \frac{1}{s} + \frac{1}{s'} \)
Magnification:
\( m = \frac{y'}{y} = -\frac{s'}{s} \)
Sign Conventions for Mirrors:
- Concave Mirror: \( f > 0 \) (converging). Can form real, inverted images or virtual, magnified upright images (when \( s < f \)).
- Convex Mirror: \( f < 0 \) (diverging). Always forms a virtual, upright, and diminished image (\( s' < 0 \), \( |m| < 1 \)).
- Object Distance (\( s \)): Positive for real objects placed in front of the mirror.
- Image Distance (\( s' \)): Positive for real images (formed in front of the mirror); negative for virtual images (formed behind the mirror).
2. Refraction and Snell's Law
Refraction occurs when light passes into a medium with a different Index of Refraction (n), altering its propagation speed and direction.
Index of Refraction (n):
\( n = \frac{c}{v} \)
Where \( c \) is the speed of light in a vacuum (\( 3.00 \times 10^8\text{ m/s} \)) and \( v \) is the phase velocity of light in the medium (with \( n \ge 1 \)).
Snell’s Law
\( n_1 \sin \theta_1 = n_2 \sin \theta_2 \)
- From lower \( n \) to higher \( n \) (e.g., air to water): Light bends toward the normal line (\( \theta_2 < \theta_1 \), \( v_2 < v_1 \)).
- From higher \( n \) to lower \( n \) (e.g., water to air): Light bends away from the normal line (\( \theta_2 > \theta_1 \), \( v_2 > v_1 \)).
Important Principle: Frequency (\( f \)) remains constant during refraction across any boundary, while wavelength changes proportionally to speed: \( v = f \lambda \implies \frac{\lambda_1}{\lambda_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1} \).
---3. Critical Angle & Total Internal Reflection
Total internal reflection can occur only when light travels from an optically denser medium (higher \( n_1 \)) to an optically less dense medium (lower \( n_2 \)).
- Critical Angle (\( \theta_c \)): The angle of incidence for which the angle of refraction is exactly \( 90^\circ \).
- Formula: \( \sin \theta_c = \frac{n_2}{n_1} \) (where \( n_1 > n_2 \)).
- Total Internal Reflection: If the angle of incidence \( \theta_1 > \theta_c \), no refraction occurs; all incident energy reflects back into the original medium.
Applications: Optical fibres, prismatic binoculars, and natural phenomena like mirages.
---4. Apparent Depth
When an observer views an object submerged in a medium of different refractive index nearly along the normal line, refraction causes the apparent depth to differ from the real depth.
Formula: \( \frac{s'}{s} = \frac{n_{\text{observer}}}{n_{\text{object}}} \)
Where \( s \) is the real depth, \( s' \) is the apparent depth, \( n_{\text{object}} \) is the refractive index of the object's medium, and \( n_{\text{observer}} \) is that of the viewing medium.
---5. Thin Lenses
Thin lenses manipulate light via refraction across two spherical surfaces.
- Convex Lens (Converging): Thicker at the centre than at the edges. Bends parallel rays inward toward the focal point.
- Concave Lens (Diverging): Thinner at the centre than at the edges. Bends parallel rays outward, diverging as if from a virtual focal point.
Lens Equation and Magnification
\( \frac{1}{f} = \frac{1}{s} + \frac{1}{s'} \)
\( m = \frac{y'}{y} = -\frac{s'}{s} \)
Sign Conventions:
- \( f > 0 \) for a convex lens; \( f < 0 \) for a concave lens.
- \( s > 0 \) for real objects.
- \( s' > 0 \) for real images (formed on the opposite side of the lens from the object); \( s' < 0 \) for virtual images (formed on the same side as the object).
- \( m > 0 \) indicates an upright (virtual) image; \( m < 0 \) indicates an inverted (real) image.
Key Takeaway: A concave lens always produces a virtual, upright, and diminished image (\( |m| < 1 \)) for any real object position.
---6. Wave Optics: Interference & Diffraction
Young's Double-Slit Interference
When coherent monochromatic light passes through two parallel slits separated by distance \( d \), interference fringes form on a screen placed at distance \( L \):
- Constructive interference (bright fringes): \( d \sin \theta = n\lambda \) or \( d\frac{x_n}{L} = n\lambda \) (where \( n = 0, 1, 2, \dots \)).
- Destructive interference (dark fringes): \( d \sin \theta = \left(n - \frac{1}{2}\right)\lambda \) (where \( n = 1, 2, 3, \dots \)).
- Fringe spacing: The distance between adjacent bright fringes is \( \Delta x = \frac{\lambda L}{d} \).
Single-Slit Diffraction
When light passes through a single narrow slit of width \( a \), diffraction causes a wide central bright band bordered by dark minima:
- Dark fringes (minima condition): \( a \sin \theta = n\lambda \) (where \( n = 1, 2, 3, \dots \)).
- The central bright maximum is twice as wide as the secondary maxima and contains the majority of the transmitted light intensity.
Diffraction Grating
A grating consists of a large number of equidistant parallel slits (\( N \) lines per unit length). The slit separation is \( d = \frac{1}{N} \).
Principal maxima condition: \( d \sin \theta = n\lambda \) (where \( n = 0, 1, 2, \dots \)).
Because \( N \) is large, the maxima are extremely sharp and widely spaced, making gratings ideal for spectral analysis.
---7. Natural Optical Phenomena & Colour Mixing
Dispersion and Rainbows
The refractive index \( n \) of transparent media varies slightly with wavelength (dispersion), with violet light bending more than red light. When sunlight enters raindrops, refraction, internal reflection, and dispersion separate white light into a spectrum, forming a rainbow.
Colour Mixing
- Additive Colour Mixing (Light): The primary colours of light are Red, Green, and Blue (RGB). Combining all three primary light colours at equal intensity yields white light. Combinations yield secondary colours: Red + Green = Yellow, Red + Blue = Magenta, Green + Blue = Cyan.
- Subtractive Colour Mixing (Pigments): Pigments absorb certain wavelengths and reflect others. The primary pigment colours are Cyan, Magenta, and Yellow. Combining all three absorbs all visible wavelengths, producing black.
Final Checklist for Exam Day
Before entering the exam hall, verify that you can:
- Apply Snell's Law and calculate the critical angle for total internal reflection.
- Use the mirror and thin-lens equations while rigorously checking your signs for \( f \), \( s \), and \( s' \).
- Solve double-slit fringe spacing and single-slit dark-fringe equations without confusing the conditions.
- Distinguish additive light mixing (RGB) from subtractive pigment mixing (CMY).