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Geometrical Optics formulas

Master Geometrical Optics through 34 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Geometrical Optics, every formula

34 formulas, typeset and free. Print it, or keep it open beside your practice.

Law of reflection
$∠ i = ∠ r$
Q1MCQReflection
For reflection at a plane mirror:
- A
  $\angle i=\angle r$
- B
  $\angle i=2\angle r$
- C
  $\angle i+\angle r=90^{\circ}$
- D
  $\angle i=0$
Mirror formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Mirror focal length
$f = \frac{R}{2}$
Transverse magnification (mirror)
$m = \frac{h _{2}}{h _{1}} = - \frac{v}{u}$
Longitudinal magnification
$m_{L} = - \frac{v ^{2}}{u ^{2}} = - m^{2}$
small object
Q1MCQLongitudinal mag
The longitudinal magnification of a small object is:
- A
  $-m^{2}$
- B
  $m$
- C
  $m^{2}$
- D
  $-m$
Mirror power
$P = - \frac{1}{f}$
Newton's formula
$X Y = f^{2}$
distances from focus
Q1MCQNewton's formula
Newton's formula for a mirror is:
- A
  $XY=f^{2}$
- B
  $X+Y=f$
- C
  $XY=f$
- D
  $X-Y=f^{2}$
Refractive index
$μ = \frac{c}{v}$
Q1MCQRefractive index
The refractive index of a medium is:
- A
  $\dfrac{c}{v}$
- B
  $\dfrac{v}{c}$
- C
  $cv$
- D
  $c-v$
Snell's law
$μ_{1} sin i = μ_{2} sin r$
Q1MCQSnell's law
Snell's law states:
- A
  $\mu_1\sin i=\mu_2\sin r$
- B
  $\mu_1\cos i=\mu_2\cos r$
- C
  $\dfrac{\sin i}{\sin r}=\mu_1\mu_2$
- D
  $\sin i=\sin r$
Deviation on refraction
$δ = i - r$
Lateral shift in a slab
$x = \frac{t sin ( i - r )}{cos r}$
Q1MCQLateral shift
The lateral shift for a ray through a slab is:
- A
  $\dfrac{t\sin(i-r)}{\cos r}$
- B
  $t\sin i$
- C
  $t\cos r$
- D
  $t(i-r)$
Apparent depth
$d^{'} = \frac{d}{μ}$
Apparent shift
$shift = d (1 - \frac{1}{μ})$
Q1MCQApparent shift
The apparent shift of an object seen through a slab is:
- A
  $d\left(1-\dfrac{1}{\mu}\right)$
- B
  $\dfrac{d}{\mu}$
- C
  $d\mu$
- D
  $d(1-\mu)$
Critical angle
$C = sin^{- 1} \frac{1}{μ}$
Q1MCQCritical angle
The critical angle for a medium of refractive index $\mu$ is:
- A
  $\sin^{-1}\dfrac{1}{\mu}$
- B
  $\sin^{-1}\mu$
- C
  $\cos^{-1}\dfrac{1}{\mu}$
- D
  $\tan^{-1}\mu$
TIR condition
$i > C (denser to rarer)$
Q1MCQTIR
Total internal reflection requires the ray to travel:
- A
  from a denser to a rarer medium with $i>C$
- B
  from rarer to denser
- C
  at $i=0$
- D
  in vacuum
Prism deviation
$δ = i + e - A$
Q1MCQPrism deviation
The deviation produced by a prism is:
- A
  $i+e-A$
- B
  $i-e+A$
- C
  $A-i-e$
- D
  $i+e+A$
Prism refraction angles
$r_{1} + r_{2} = A$
Q1MCQPrism angles
For a prism, the refraction angles satisfy:
- A
  $r_1+r_2=A$
- B
  $r_1-r_2=A$
- C
  $r_1=r_2$
- D
  $r_1 r_2=A$
Minimum deviation
$δ_{m i n} = 2 i - A$
i=e, r_1=r_2
Q1MCQMin deviation
At minimum deviation through a prism:
- A
  $i=e$ and $r_1=r_2$
- B
  $i=90^{\circ}$
- C
  $e=0$
- D
  $r_1=0$
Prism refractive index
$μ = \frac{sin ( \frac{A + δ _{m i n}}{2} )}{sin ( \frac{A}{2} )}$
Q1MCQPrism μ
The refractive index of a prism material is:
- A
  $\dfrac{\sin\!\left(\tfrac{A+\delta_{\min}}{2}\right)}{\sin\!\left(\tfrac{A}{2}\right)}$
- B
  $\dfrac{\sin A}{\sin\delta_{\min}}$
- C
  $\sin\!\left(\tfrac{A+\delta_{\min}}{2}\right)$
- D
  $\dfrac{A}{\delta_{\min}}$
Thin prism deviation
$δ = (μ - 1) A$
Angular dispersion
$θ = (μ_{v} - μ_{r}) A$
Q1MCQAngular dispersion
The angular dispersion of a thin prism is:
- A
  $(\mu_v-\mu_r)A$
- B
  $(\mu_y-1)A$
- C
  $(\mu_v+\mu_r)A$
- D
  $\mu A$
Dispersive power
$ω = \frac{μ _{v} - μ _{r}}{μ _{y} - 1}$
Q1MCQDispersive power
The dispersive power of a prism material is:
- A
  $\dfrac{\mu_v-\mu_r}{\mu_y-1}$
- B
  $\dfrac{\mu_y-1}{\mu_v-\mu_r}$
- C
  $(\mu_v-\mu_r)$
- D
  $(\mu_y-1)$
Refraction at a spherical surface
$\frac{μ _{2}}{v} - \frac{μ _{1}}{u} = \frac{μ _{2} - μ _{1}}{R}$
Q1MCQSpherical surface
For refraction at a spherical surface:
- A
  $\dfrac{\mu_2}{v}-\dfrac{\mu_1}{u}=\dfrac{\mu_2-\mu_1}{R}$
- B
  $\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$
- C
  $\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$
- D
  $\mu_1 v=\mu_2 u$
Lens formula
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
Lens magnification
$m = \frac{v}{u}$
Q1MCQLens magnification
The magnification of a lens is:
- A
  $\dfrac{v}{u}$
- B
  $-\dfrac{v}{u}$
- C
  $\dfrac{u}{v}$
- D
  $vu$
Lens maker's formula
$\frac{1}{f} = (μ - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$
Q1MCQLens maker
The lens maker's formula is:
- A
  $\dfrac{1}{f}=(\mu-1)\left(\dfrac{1}{R_1}-\dfrac{1}{R_2}\right)$
- B
  $\dfrac{1}{f}=\dfrac{\mu}{R}$
- C
  $f=(\mu-1)R$
- D
  $\dfrac{1}{f}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$
Power of a lens
$P = \frac{1}{f ( m )} = \frac{100}{f ( cm )}$
Lenses in contact
$P = P_{1} + P_{2}$
Lenses separated by d
$\frac{1}{F} = \frac{1}{f _{1}} + \frac{1}{f _{2}} - \frac{d}{f _{1} f _{2}}$
Q1MCQLenses separated
For two lenses separated by $d$:
- A
  $\dfrac{1}{F}=\dfrac{1}{f_1}+\dfrac{1}{f_2}-\dfrac{d}{f_1 f_2}$
- B
  $\dfrac{1}{F}=\dfrac{1}{f_1}+\dfrac{1}{f_2}$
- C
  $F=f_1+f_2$
- D
  $\dfrac{1}{F}=\dfrac{d}{f_1 f_2}$
Silvered lens (plane silvered)
$f = \frac{R}{2 ( μ - 1 )}$
Q1MCQSilvered lens
For a plano-convex lens with its plane face silvered, the effective focal length is:
- A
  $\dfrac{R}{2(\mu-1)}$
- B
  $\dfrac{R}{2\mu}$
- C
  $\dfrac{R}{2}$
- D
  $R(\mu-1)$
Simple microscope (near point)
$M P = 1 + \frac{D}{f}$
Q1MCQSimple microscope
The magnifying power of a simple microscope (image at near point) is:
- A
  $1+\dfrac{D}{f}$
- B
  $\dfrac{D}{f}$
- C
  $\dfrac{f}{D}$
- D
  $1-\dfrac{D}{f}$
Compound microscope
$M P = \frac{v _{0}}{u _{0}} (1 + \frac{D}{f _{e}})$
Q1MCQCompound microscope
The magnifying power of a compound microscope (near point) is:
- A
  $\dfrac{v_0}{u_0}\left(1+\dfrac{D}{f_e}\right)$
- B
  $\dfrac{f_0}{f_e}$
- C
  $\dfrac{D}{f_e}$
- D
  $\dfrac{v_0}{u_0}$
Astronomical telescope
$M P = \frac{f _{0}}{f _{e}}, L = f_{0} + f_{e}$
Q1MCQTelescope
The magnifying power of an astronomical telescope (normal adjustment) is:
- A
  $\dfrac{f_0}{f_e}$
- B
  $\dfrac{f_e}{f_0}$
- C
  $f_0 f_e$
- D
  $f_0+f_e$
Resolving power (telescope)
$R = \frac{a}{1.22 λ}$
Q1MCQResolving power
The resolving power of a telescope is:
- A
  $\dfrac{a}{1.22\lambda}$
- B
  $\dfrac{1.22\lambda}{a}$
- C
  $\dfrac{2\mu\sin\theta}{\lambda}$
- D
  $\dfrac{\lambda}{a}$

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Geometrical Optics formulas

Geometrical Optics, every formula

Law of reflection

Mirror formula

Mirror focal length

Transverse magnification (mirror)

Longitudinal magnification

Mirror power

Newton's formula

Refractive index

Snell's law

Deviation on refraction

Lateral shift in a slab

Apparent depth

Apparent shift

Critical angle

TIR condition

Prism deviation

Prism refraction angles

Minimum deviation

Prism refractive index

Thin prism deviation

Angular dispersion

Dispersive power

Refraction at a spherical surface

Lens formula

Lens magnification

Lens maker's formula

Power of a lens

Lenses in contact

Lenses separated by d

Silvered lens (plane silvered)

Simple microscope (near point)

Compound microscope

Astronomical telescope

Resolving power (telescope)

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