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Ray Optics formula sheet

Every formula in the Ray Optics chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 58 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Reflection and plane mirrors

Law of reflection (vector form)
2× asked, last 2023
b^=a^−2(a^⋅n^) n^\hat b=\hat a-2(\hat a\cdot\hat n)\,\hat n
a^\hat a, b^\hat b: incident and reflected unit vectors; n^\hat n: unit normal. i=ri=r.
Deviation by one reflection
δ=180∘−2i\delta=180^\circ-2i
ii measured from the normal.
Rotating mirror
mirror turns θ ⇒ reflected ray turns 2θ\text{mirror turns }\theta\ \Rightarrow\ \text{reflected ray turns }2\theta
Incident ray kept fixed.
Image velocity in a plane mirror
3× asked, last 2023
vI⊥=2vM⊥−vO⊥,vI∥=vO∥v_{I\perp}=2v_{M\perp}-v_{O\perp},\qquad v_{I\parallel}=v_{O\parallel}
⊥\perp: along the normal, ∥\parallel: along the mirror. Mirror moves dd, image moves 2d2d.
Least mirror height to see yourself
Lmin⁡=H2L_{\min}=\frac H2
HH = your height. Any distance from the mirror; lower edge at half your eye height.
Images in two inclined mirrors
3× asked, last 2023
m=360∘θ,n=m−1  (m even)m=\frac{360^\circ}{\theta},\qquad n=m-1\ \ (m\text{ even})
mm odd: m−1m-1 images if the object is on the bisector, mm if not. Parallel mirrors: infinitely many.
Deviation by two inclined mirrors
δ=360∘−2θ\delta=360^\circ-2\theta
One reflection at each mirror; does not depend on ii.

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51 more formulas in 6 topics

Spherical mirrors, Refraction and total internal reflection, Spherical surfaces and thin lenses, Lens combinations and multi-element systems, Prism and dispersion and Optical instruments. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Spherical mirrors

  • Mirror formula15×
  • Focal length
  • Magnification10×
  • Magnification from ff
  • Object along the axis (mirror)6×

Refraction and total internal reflection

  • Snell's law12×
  • Refractive index
  • Speed and wavelength in a medium7×
  • Time through a slab
  • Apparent depth10×
  • Normal shift
  • Lateral shift in a slab4×
  • Critical angle14×
  • Right-angled 45° prism (TIR)
  • Circle of light from a source under water2×
  • Fraction of light that escapes
  • Optical fibre: largest entry angle2×

Spherical surfaces and thin lenses

  • Refraction at a spherical surface14×
  • Magnification at one surface
  • Glass sphere: focus
  • Thin lens formula10×
  • Lens magnification
  • Equal-sized images
  • Lensmaker's formula12×
  • Equiconvex and plano-convex
  • Lens in a medium10×
  • Newton's formula6×
  • Cutting a lens
  • Displacement method1×

Lens combinations and multi-element systems

  • Power of a lens11×
  • Lenses in contact
  • Lenses a distance dd apart4×
  • Two-step imaging14×
  • Silvered lens4×
  • Silvered plano-convex lens

Prism and dispersion

  • Refraction through a prism8×
  • Minimum deviation18×
  • Thin prism7×
  • No emergent ray
  • Angular dispersion5×
  • Dispersive power
  • Cauchy's relation
  • Deviation without dispersion5×
  • Dispersion without deviation

Optical instruments

  • Magnifying power
  • Simple microscope
  • Compound microscope7×
  • Microscope: lens separation
  • Astronomical telescope4×
  • Telescope, image at the near point
  • Reflecting telescope

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