Ray Optics — JEE Mains Physics

Formulas (3)

• Reflection at a plane mirror · Reflection at a plane mirror
  $$\delta = 180^{\circ} - 2i, \qquad \hat b = \hat a - 2(\hat a\cdot\hat n)\hat n, \qquad n = \frac{360^{\circ}}{\theta} - 1$$
• The mirror formula and magnification · Mirror formula
  $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, \qquad f = \frac{R}{2}, \qquad m = -\frac{v}{u} = \frac{f}{f - u}$$
• Image speed for a moving object · Image speed along the axis
  $$\frac{dv}{dt} = -m^{2}\frac{du}{dt}, \qquad m = \frac{f}{f - u}$$

Watch out for (10)

• Deviation is not the angle of reflection
  → Reflection at a plane mirror
• Moving the mirror is not moving the object
  → Reflection at a plane mirror
• A plane-mirror image is erect
  → Reflection at a plane mirror
• m = −v/u for a mirror, v/u for a lens
  → The mirror formula and magnification
• An erect, smaller image means a convex mirror
  → The mirror formula and magnification
• A mirror's focal length does not depend on the medium
  → The mirror formula and magnification
• Two positions, two kinds of image
  → The mirror formula and magnification
• Along the axis, speed scales with m², not m
  → Image speed for a moving object
• A long rod is not a short object
  → Image speed for a moving object
• Use the speed relative to the mirror
  → Image speed for a moving object

Formulas (2)

• Snell's law and the parallel slab · Snell's law and lateral shift
  $$n_1\sin i = n_2\sin r, \qquad n = \frac{c}{v}, \qquad d = \frac{t\sin(i - r)}{\cos r}$$
• Apparent depth and the normal shift · Apparent depth
  $$d_{\text{app}} = \frac{d}{\mu}, \qquad \text{shift} = d\left(1 - \frac{1}{\mu}\right), \qquad d_{\text{app}} = \sum \frac{d_i}{\mu_i}$$

Watch out for (6)

• Angles are measured from the normal
  → Snell's law and the parallel slab
• A slab shifts a ray but does not turn it
  → Snell's law and the parallel slab
• Refractive index is not mass density
  → Snell's law and the parallel slab
• The shift is not the apparent depth
  → Apparent depth and the normal shift
• Never average the indices of a stack
  → Apparent depth and the normal shift
• Looking up multiplies, looking down divides
  → Apparent depth and the normal shift

Formulas (2)

• Critical angle · Critical angle
  $$\sin C = \frac{n_{\text{rarer}}}{n_{\text{denser}}} = \frac{v_{\text{denser}}}{v_{\text{rarer}}}, \qquad n = \sqrt{\mu_r\varepsilon_r}$$
• Total internal reflection in tanks, blocks and prisms · Circle of light and a coated face
  $$r = h\tan C = \frac{h}{\sqrt{\mu^{2} - 1}}, \qquad \sin C = \frac{n_2}{n}\ (\text{coated face})$$

Watch out for (6)

• No total reflection from rarer to denser
  → Critical angle
• The slower medium is the denser one
  → Critical angle
• At i = C the light is not yet trapped
  → Critical angle
• The circle's radius uses tan C
  → Total internal reflection in tanks, blocks and prisms
• A coating raises the critical angle
  → Total internal reflection in tanks, blocks and prisms
• A 'minimum index for total reflection' may be a maximum
  → Total internal reflection in tanks, blocks and prisms

Formulas (2)

• Refraction at a single spherical surface · Single spherical surface
  $$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}, \qquad m = \frac{\mu_1 v}{\mu_2 u}$$
• Lens-maker's formula · Lens-maker's formula
  $$\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \qquad P = \frac{1}{f}$$

Watch out for (6)

• Each distance carries its own index
  → Refraction at a single spherical surface
• The sign of R depends on where the centre is
  → Refraction at a single spherical surface
• The magnification has the indices too
  → Refraction at a single spherical surface
• R₂ of a biconvex lens is negative
  → Lens-maker's formula
• A flat face has 1/R = 0, not R = 0
  → Lens-maker's formula
• μ − 1 is for a lens in air
  → Lens-maker's formula

Formulas (2)

• Thin lens formula and magnification · Thin lens formula
  $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, \qquad m = \frac{v}{u} = \frac{f}{f + u}, \qquad P = \frac{1}{f}$$
• Combinations of lenses · Lenses in combination
  $$P = P_1 + P_2 - dP_1P_2, \qquad m = m_1 m_2$$

Watch out for (6)

• The lens formula has a minus sign
  → Thin lens formula and magnification
• A concave lens never forms a real image of a real object
  → Thin lens formula and magnification
• A long or slanted object needs two magnifications
  → Thin lens formula and magnification
• A virtual object has u > 0
  → Combinations of lenses
• Measure from the next lens
  → Combinations of lenses
• Powers add only in contact
  → Combinations of lenses

Formulas (2)

• A lens in a liquid · Lens in a medium
  $$\frac{1}{f_m} = \left(\frac{\mu_l}{\mu_m} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \qquad \frac{f_m}{f_{\text{air}}} = \frac{\mu_l - 1}{\mu_l/\mu_m - 1}$$
• A silvered lens as a mirror · Silvered lens
  $$P = 2P_L + P_M, \qquad F = \frac{1}{P}, \qquad F = \frac{f_L}{2}\ (\text{plane face silvered})$$

Reference tables (1)

Watch out for (8)

• The radii stay; only the factor changes
  → A lens in a liquid
• A convex lens can diverge
  → A lens in a liquid
• Use the ratio of the factors
  → A lens in a liquid
• A smaller lens is not a weaker lens
  → Focal length of the pieces of a cut lens
• Across the axis, the power halves
  → Focal length of the pieces of a cut lens
• The lens counts twice
  → A silvered lens as a mirror
• A silvered plane face adds no power
  → A silvered lens as a mirror
• The silvered curved face is concave from inside
  → A silvered lens as a mirror

Formulas (3)

• Prism and minimum deviation · Prism and minimum deviation
  $$r_1 + r_2 = A, \qquad \delta = i + e - A, \qquad \mu = \frac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}}$$
• Grazing emergence from a prism · Grazing emergence
  $$\sin r_2 = \frac{1}{\mu}\ (e = 90^{\circ}), \qquad r_1 = A - r_2, \qquad \sin i = \mu\sin r_1$$
• Thin prisms and dispersion · Thin prism and dispersion
  $$\delta = (\mu - 1)A, \qquad (\mu_1 - 1)A_1 = (\mu_2 - 1)A_2, \qquad \omega = \frac{\mu_v - \mu_r}{\mu_y - 1}$$

Watch out for (8)

• Use A/2 inside, not A
  → Prism and minimum deviation
• Through a prism the deviation is i + e − A
  → Prism and minimum deviation
• Two angles of incidence give the same deviation
  → Prism and minimum deviation
• Grazing emergence fixes r₂, not i
  → Grazing emergence from a prism
• A coating changes the critical angle at that face only
  → Grazing emergence from a prism
• The prisms face opposite ways
  → Thin prisms and dispersion
• δ = (μ − 1)A is for thin prisms only
  → Thin prisms and dispersion
• Red bends least
  → Thin prisms and dispersion

Reference tables (2)

Watch out for (6)

• A telescope's M is fₒ/fₑ, not fₑ/fₒ
  → Magnification of microscopes and telescopes
• A wider objective does not raise the magnification
  → Magnification of microscopes and telescopes
• Normal adjustment uses D/fₑ, not 1 + D/fₑ
  → Magnification of microscopes and telescopes
• Resolving power is not magnification
  → Resolving power and defects of vision
• A reading glass forms a virtual image
  → Resolving power and defects of vision
• Blurred is not the same as distorted
  → Resolving power and defects of vision