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Class 12 Physics Notes

Ray Optics and Optical Instruments Class 12 Physics Notes

Complete, exam-ready notes on ray optics and optical instruments: reflection, refraction and Snell's law, spherical mirrors, lenses and the lens maker formula, total internal reflection, prisms, and the microscope and telescope — written for CBSE boards, JEE and NEET revision.

Class12SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is Snell's law in one line?

Snell's law relates the angles of incidence and refraction to the refractive indices of two media: n₁ sinθ₁ = n₂ sinθ₂, where n = c/v is the refractive index.

Reflection and Spherical Mirrors

Mirror formula

1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

For a spherical mirror of focal length f = R/2, object distance u and image distance v. Magnification m=−vum = -\frac{v}{u}. Sign convention: distances to the left of the mirror are negative.

  • Concave mirrors converge light (real, inverted images); convex mirrors diverge (virtual, erect, diminished — useful as rear-view mirrors).
  • Focal length:
  • f=R2f = \frac{R}{2}
  • .
1f=1u+1v,m=−vu\frac{1}{f} = \frac{1}{u} + \frac{1}{v},\quad m = -\frac{v}{u}
Mirror formula

Refraction and Snell's Law

Snell's law

n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1 = n_2\sin\theta_2

The refractive index of a medium is n = c/v. When light travels from a rarer to a denser medium it bends toward the normal; from denser to rarer it bends away.

Total internal reflection

When light travels from a denser to a rarer medium at an angle beyond the critical angle sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}, it is totally reflected back. This powers optical fibres and produces mirages.

Lenses and the Lens Maker Formula

Lens maker formula

1f=(n−1)(1R1−1R2)\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)

Relates the focal length of a thin lens to its refractive index n and the radii of curvature of its two surfaces. A converging (convex) lens has positive f; a diverging (concave) lens has negative f.

  • Lens formula:
  • 1f=1v−1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
  • .
  • Power of a lens:
  • P=1f (m)P = \frac{1}{f\,(m)}
  • in dioptres; powers add for combined lenses.
  • The human eye's lens changes shape (accommodation) to focus on near and far objects.
1f=(n−1)(1R1−1R2),P=1f\frac{1}{f} = (n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right),\quad P = \frac{1}{f}
Lens maker formula and power

Prisms and Dispersion

Prism formula

δ=i1+i2−A\delta = i_1 + i_2 - A

The angle of deviation δ depends on the angle of incidence and the prism angle A. At minimum deviation the ray travels symmetrically: n=sin⁡A+δm2sin⁡A2n = \frac{\sin\frac{A+\delta_m}{2}}{\sin\frac{A}{2}}.

  • Dispersion splits white light because different wavelengths have slightly different refractive indices.
  • The deviation is minimum when the light passes symmetrically through the prism.

Optical Instruments

  • Simple microscope: a single convex lens, magnification
  • m=1+Dfm = 1 + \frac{D}{f}
  • (D = near point, 25 cm).
  • Compound microscope: magnification is the product of objective and eyepiece magnifications.
  • Telescope: magnifies distant objects; angular magnification
  • M=fofeM = \frac{f_o}{f_e}
  • for relaxed eye.
  • The eye: far point at infinity, near point about 25 cm, focal length adjusts by accommodation.
msimple=1+Df,Mtelescope=fofem_{\text{simple}} = 1 + \frac{D}{f},\quad M_{\text{telescope}} = \frac{f_o}{f_e}
Magnification of instruments

Solved Examples

Example: A convex lens has focal length 20 cm20\,\text{cm}. Find its power.

Solution: P=10.2=5 DP = \frac{1}{0.2} = 5\,\text{D}.

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Snell's law

n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1 = n_2\sin\theta_2

Mirror formula

1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

Lens maker formula

1f=(n−1)(1R1−1R2)\frac{1}{f} = (n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)

Power of lens

P=1fP = \frac{1}{f}

Critical angle

sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}

Telescope magnification

M=fofeM = \frac{f_o}{f_e}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • Snell's law: n₁sinθ₁ = n₂sinθ₂.
  • Mirror formula and lens formula differ in sign for u.
  • Lens maker: 1/f = (n−1)(1/R₁ − 1/R₂).
  • Total internal reflection above the critical angle.
  • Telescope magnification = fo/fe.

FAQ

Common questions

What is total internal reflection?

When a ray travelling from a denser to a rarer medium strikes the interface at an angle greater than the critical angle, it is fully reflected back. Optical fibres rely on it.

What is the difference between a concave and convex mirror?

A concave mirror converges light and can form real, inverted images; a convex mirror diverges light and always forms virtual, erect, diminished images (used as rear-view mirrors).

What does the lens maker formula give?

The focal length of a thin lens from its refractive index and the radii of curvature of its surfaces: 1/f = (n−1)(1/R₁ − 1/R₂).

How does a compound microscope magnify?

The objective forms a real, magnified image, and the eyepiece further magnifies it — the total magnification is the product of the two.

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