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MHT-CET Physics · Formula sheet

Optics (Ray) formulas

9 formulas and 13 common traps for MHT-CET Physics Optics (Ray), grouped by subtopic.

Full notes with worked examples

Mirrors

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The Mirror Formula and Plane Mirrors

Mirror formula

1v+1u=1f,m=−vu\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, \qquad m = -\frac{v}{u}

Common traps

Thinking a half-covered mirror forms half an image

Every part of the mirror receives light from every point of the object. Covering half removes half the light, not half the picture.

Refraction, Apparent Depth and Total Internal Reflection

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Snell's Law and the Refractive Index

Snell's law

sin⁡i=μsin⁡r,μ=cv\sin i = \mu\sin r, \qquad \mu = \frac{c}{v}

Apparent Depth and Normal Shift

Apparent depth

dapp=dμ,shift=d(1−1μ)d_{\text{app}} = \frac{d}{\mu}, \qquad \text{shift} = d\left(1 - \frac{1}{\mu}\right)

Total Internal Reflection

Critical angle

sin⁡C=1μ,rdisc=hμ2−1\sin C = \frac{1}{\mu}, \qquad r_{\text{disc}} = \frac{h}{\sqrt{\mu^2 - 1}}

Common traps

Taking μ as the fraction of speed kept

Speed reduced by 25% means v = 0.75c and μ = 1/0.75 = 4/3 — not 0.75.

Multiplying by μ instead of dividing

Objects in a denser medium look NEARER. Apparent depth is the real depth divided by μ.

Allowing total internal reflection from rarer to denser

Entering a denser medium the ray bends toward the normal and always gets through. Total internal reflection needs denser to rarer.

Giving red the smaller critical angle

Red has the smallest refractive index, so the LARGEST critical angle. Blue and violet are totally reflected first.

The Prism: Deviation and Dispersion

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Deviation and Minimum Deviation

Prism

μ=sin⁡A+δm2sin⁡A2,δthin=(μ−1)A\mu = \frac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}}, \qquad \delta_{\text{thin}} = (\mu - 1)A

Dispersion, Dispersive Power and Achromatism

Dispersive power

ω=δV−δRδY,ω1P1+ω2P2=0\omega = \frac{\delta_V - \delta_R}{\delta_Y}, \qquad \omega_1P_1 + \omega_2P_2 = 0

Common traps

Using the glass's own index in water

In water the prism bends light by the RELATIVE index, μ_glass/μ_water = 9/8. The deviation drops from 0.5A to A/8.

Forgetting that a retracing ray meets the silvered face normally

To come straight back, the ray inside must hit the silvered face at 90°, so r₁ equals the prism angle A.

Dividing by the violet or red deviation

Dispersive power divides the spread by the MEAN (yellow) deviation. Using δ_V or δ_R changes the ratio of two prisms.

Lenses: the Lens Formula, the Lensmaker's Equation and Combinations

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The Lens Formula and Magnification

Lens formula

1v−1u=1f,m=vu\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, \qquad m = \frac{v}{u}

Lensmaker's Equation and Combining Lenses

Lensmaker and combinations

1f=(μ−1)(1R1−1R2),P=P1+P2−dP1P2\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \qquad P = P_1 + P_2 - dP_1P_2

Common traps

Taking v = nu for a real image in a lens

A lens's real image is on the OTHER side, so v and u have opposite signs: v = −nu. Using v = nu gives (n − 1) where the answer has (n + 1).

Adding focal lengths instead of powers

Lenses in contact add POWERS, 1/f. A 40 cm convex with a 25 cm concave gives 2.5 − 4 = −1.5 D, not 15 cm.

Using centimetres in the power

Power in dioptres is 1/f with f in METRES: 100/f with f in cm.

The Microscope and the Telescope

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Magnifying Power and Resolution

Magnifying power

Mmicro=v0u0⋅Dfe,Mtele=f0feM_{\text{micro}} = \frac{v_0}{u_0}\cdot\frac{D}{f_e}, \qquad M_{\text{tele}} = \frac{f_0}{f_e}

Common traps

Thinking a large aperture raises the magnification

Magnification is set by focal lengths. A large aperture collects more light and resolves finer detail.

Using the full tube length as the objective's image distance

For a relaxed eye the intermediate image sits at the eyepiece's focus, so v₀ = L − fₑ.

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