Optics | CBSE - Wyatt's Notes

sources:

• text: Standard textbook reference

Optics studies the behavior of light, including reflection, refraction, diffraction, and interference. It covers mirrors, lenses, optical instruments, and wave optics.

• Reflection: angle of incidence = angle of reflection
• Snell’s law: $n_1\sin\theta_1 = n_2\sin\theta_2$
• Mirror equation: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
• Lens equation: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ (sign convention: $u$ is negative for real objects)
• Magnification: $m = -\frac{v}{u}$ (mirror), $m = \frac{v}{u}$ (lens)
• Critical angle: $\sin\theta_c = \frac{n_2}{n_1}$ (for total internal reflection)
• Young’s double slit: fringe width $\beta = \frac{\lambda D}{d}$

Problem: An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find the image position and magnification.

Solution:

Using the mirror equation: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

For a concave mirror, $f = -15$ cm (negative by sign convention). Object distance $u = -30$ cm (negative).

$\frac{1}{-15} = \frac{1}{v} + \frac{1}{-30}$

$\frac{1}{v} = \frac{1}{-15} + \frac{1}{30} = \frac{-2 + 1}{30} = \frac{-1}{30}$

$v = -30 \, \text{cm}$

The image is at 30 cm in front of the mirror (same side as object).

Magnification: $m = -\frac{v}{u} = -\frac{-30}{-30} = -1$

The image is real, inverted, and the same size as the object.

Common mistake: Forgetting the sign convention. For mirrors, $f$ is negative for concave mirrors (when the object is outside the focal point).

Problem: A convex lens of focal length 20 cm forms a real image at 60 cm from the lens. Find the object distance and magnification.

Solution:

Using the lens equation: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

For a convex lens, $f = +20$ cm. Image distance $v = +60$ cm (positive for real image).

$\frac{1}{20} = \frac{1}{60} - \frac{1}{u}$

$\frac{1}{u} = \frac{1}{60} - \frac{1}{20} = \frac{1 - 3}{60} = \frac{-2}{60} = \frac{-1}{30}$

$u = -30 \, \text{cm}$

The object is 30 cm in front of the lens.

Magnification: $m = \frac{v}{u} = \frac{60}{-30} = -2$

The image is real, inverted, and twice the size of the object.

Common mistake: Using the mirror equation for lenses. The lens equation has a minus sign between $1/v$ and $1/u$.

Problem: A ray of light travels from glass ($n = 1.5$) to air. Find the critical angle for total internal reflection.

Solution:

Using the critical angle formula: $\sin\theta_c = \frac{n_2}{n_1} = \frac{1}{1.5} = \frac{2}{3}$

$\theta_c = \sin^{-1}\left(\frac{2}{3}\right) \approx 41.8°$

For any angle of incidence greater than $41.8°$, total internal reflection occurs.

Common mistake: Reversing the ratio. The critical angle is defined for light going from a denser medium to a rarer medium, so $n_1 > n_2$.

1. A concave mirror of focal length 10 cm creates an image at 30 cm. Find the object distance and magnification.
2. A convex lens of focal length 15 cm forms an image at 45 cm. Find the object distance.
3. Calculate the critical angle for light going from water ($n = 1.33$) to air.

• Draw ray diagrams for mirrors and lenses
• Use sign convention consistently (Cartesian sign convention)
• For total internal reflection, light must go from denser to rarer medium
• Practice with both real and virtual images
• Remember that convex lenses and concave mirrors form real images when the object is beyond the focal point

The mirror equation is $1/f = 1/v + 1/u$ while the lens equation is $1/f = 1/v - 1/u$. The sign of the $1/u$ term differs between the two. Students often use the same equation for both, leading to incorrect results. A useful check: for a concave mirror, $f$ is positive; for a convex lens, $f$ is positive. Apply the Cartesian sign convention consistently.

A real image is formed where light rays actually converge and can be projected on a screen. A virtual image is formed where light rays appear to diverge from and cannot be projected. Concave mirrors and convex lenses form real images when the object is beyond the focal point. Students sometimes assume all images formed by lenses are real, which is incorrect when the object is within the focal length.

Light follows the rules of geometry — until it doesn’t: Geometric optics treats light as rays that bounce off mirrors and bend through lenses, following simple rules like “angle in equals angle out” for reflection. Think of a mirror as a perfect rebounder — every ray bounces at the same angle it arrived. Lenses are like traffic controllers for light — they bend rays so they converge (convex lens) or diverge (concave lens), focusing images onto screens or into your eyes. Wave optics reveals that light also behaves as a wave, producing interference patterns like ripples overlapping in a pond.

Why it matters: Optics is the science behind eyeglasses, cameras, microscopes, telescopes, fiber optics, and laser surgery. Understanding how light bends and reflects lets us design instruments that extend human vision from the microscopic to the cosmic scale.

The key insight: The sign convention in optics isn’t arbitrary — it encodes the physics of real vs. virtual images and ensures the mirror and lens equations work universally, but you must apply it consistently or you’ll get nonsensical results.

• Electrostatics: Electric fields influence the propagation of light through materials (electro-optic effects), connecting optics to electrostatics.
• Magnetic Effects: Electromagnetic theory unifies optics with electricity and magnetism — light is an electromagnetic wave.
• Dual Nature: Wave optics (interference, diffraction) reveals light’s wave nature, while the photoelectric effect shows its particle nature.
• Derivatives (Mathematics): Calculus is used to derive lens equations and analyze ray paths mathematically.

Total internal reflection (TIR) only occurs when light travels from a medium with higher refractive index to one with lower refractive index, and the angle of incidence exceeds the critical angle. Students sometimes apply TIR to light going from air to water, which is impossible. The critical angle formula $\sin\theta_c = n_2/n_1$ assumes $n_1 > n_2$.