Level 1 — RecognitionOptics

Optics

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Level 1: Recognition Test

Time Limit: 20 minutes Total Marks: 30

Section A — Multiple Choice Questions (1 mark each)

Choose the single best answer.

Q1. The mirror equation is: (a) $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ (b) $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ (c) $\frac{1}{v}+\frac{1}{u}=\frac{2}{f}$ (d) $v+u=f$

Q2. For a light ray passing from a denser to a rarer medium, total internal reflection occurs when the angle of incidence: (a) equals the critical angle (b) is less than the critical angle (c) exceeds the critical angle (d) is zero

Q3. The power of a lens of focal length $-25$ cm is: (a) $+4$ D (b) $-4$ D (c) $+0.25$ D (d) $-0.04$ D

Q4. In Young's double-slit experiment, the fringe width $\beta$ is given by: (a) $\frac{\lambda D}{d}$ (b) $\frac{d D}{\lambda}$ (c) $\frac{\lambda d}{D}$ (d) $\frac{D}{\lambda d}$

Q5. Brewster's angle $\theta_B$ for a medium of refractive index $n$ satisfies: (a) $\sin\theta_B = n$ (b) $\tan\theta_B = n$ (c) $\cos\theta_B = n$ (d) $\tan\theta_B = 1/n$

Q6. Snell's law can be derived from: (a) Newton's laws (b) Fermat's principle of least time (c) Coulomb's law (d) Gauss's law

Q7. In Malus's law, the transmitted intensity through an analyser is: (a) $I_0\sin^2\theta$ (b) $I_0\cos\theta$ (c) $I_0\cos^2\theta$ (d) $I_0\tan^2\theta$

Q8. For a single slit of width $a$ , the first minimum in the diffraction pattern occurs at: (a) $a\sin\theta=\lambda$ (b) $a\sin\theta=\lambda/2$ (c) $a\sin\theta=2\lambda$ (d) $a\cos\theta=\lambda$

Q9. According to Huygens' principle, every point on a wavefront acts as a source of: (a) plane waves (b) secondary wavelets (c) longitudinal waves (d) shock waves

Q10. The condition for principal maxima in a diffraction grating of spacing $d$ is: (a) $d\sin\theta=(2n+1)\lambda/2$ (b) $d\sin\theta=n\lambda$ (c) $d\cos\theta=n\lambda$ (d) $d\sin\theta=n\lambda/2$

Section B — Matching (1 mark each row; 6 marks)

Q11. Match Column I with Column II:

Column I	Column II
(i) Rayleigh criterion	(P) $\mu = \frac{1}{\sin\theta_c}$
(ii) Lens maker's equation	(Q) angular resolution $\theta=1.22\lambda/D$
(iii) Critical angle	(R) two polarized rays
(iv) Birefringence	(S) $\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
(v) Chromatic aberration	(T) coincidence of dark central spot
(vi) Newton's rings	(U) dependence of $\mu$ on wavelength

Section C — True/False WITH Justification (2 marks each; 14 marks)

State True or False and give a one-line reason. 1 mark answer + 1 mark justification.

Q12. A plane mirror always forms a real image.

Q13. The critical angle is larger for a medium of higher refractive index (relative to air).

Q14. When two thin lenses are in contact, the net power equals the sum of individual powers.

Q15. In thin-film interference by reflection, a phase change of $\pi$ occurs when light reflects off a rarer medium.

Q16. In a compound microscope, the objective forms a magnified virtual image.

Q17. For light incident at Brewster's angle, the reflected and refracted rays are perpendicular.

Q18. Diffraction effects become more pronounced as slit width increases relative to wavelength.

Answer keyMark scheme & solutions

Section A

Q1. (b) — Standard mirror equation $\frac1v+\frac1u=\frac1f$ . (1)

Q2. (c) — TIR requires $i>\theta_c$ and light going denser→rarer. (1)

Q3. (b) — $P=\frac{1}{f(\text{m})}=\frac{1}{-0.25}=-4$ D. (1)

Q4. (a) — $\beta=\frac{\lambda D}{d}$ from path-difference geometry. (1)

Q5. (b) — Brewster's law $\tan\theta_B=n$ . (1)

Q6. (b) — Snell's law derived by minimizing optical path (least time). (1)

Q7. (c) — Malus: $I=I_0\cos^2\theta$ . (1)

Q8. (a) — First minimum: $a\sin\theta=\lambda$ . (1)

Q9. (b) — Secondary wavelets (Huygens). (1)

Q10. (b) — Grating maxima: $d\sin\theta=n\lambda$ . (1)

Section B

Q11. (1 each)

(i) → Q (Rayleigh: $\theta=1.22\lambda/D$ )
(ii) → S (lens maker's equation)
(iii) → P (critical angle $\mu=1/\sin\theta_c$ )
(iv) → R (birefringence: ordinary + extraordinary rays)
(v) → U ( $\mu$ varies with wavelength)
(vi) → T (central dark spot in Newton's rings)

Section C

Q12. False (1). A plane mirror always forms a virtual, erect image behind the mirror (rays only appear to diverge from it). (1)

Q13. False (1). Since $\sin\theta_c=1/\mu$ , higher $\mu$ gives smaller critical angle. (1)

Q14. True (1). Powers add: $P=P_1+P_2$ for thin lenses in contact (from $\frac1f=\frac1{f_1}+\frac1{f_2}$ ). (1)

Q15. False (1). The $\pi$ phase change occurs when reflecting off a denser (higher-index) medium, not a rarer one. (1)

Q16. False (1). The objective forms a magnified real image; the eyepiece then magnifies it to a virtual image. (1)

Q17. True (1). At Brewster's angle $\theta_B+\theta_r=90^\circ$ , so reflected and refracted rays are perpendicular. (1)

Q18. False (1). Diffraction becomes more pronounced as slit width decreases toward the wavelength (larger $\lambda/a$ ). (1)

[
  {"claim":"Power of lens f=-25cm is -4 D","code":"f=-0.25; result = (1/f == -4)"},
  {"claim":"Brewster angle: refracted+reflected perpendicular means tan(thetaB)=n","code":"import sympy as sp; tB=sp.symbols('tB'); n=sp.symbols('n',positive=True); expr=sp.tan(tB)-n; result = sp.simplify(expr.subs(tB, sp.atan(n)))==0"},
  {"claim":"Critical angle: higher mu gives smaller theta_c","code":"import sympy as sp; tc1=sp.asin(1/sp.Rational(3,2)); tc2=sp.asin(1/sp.Rational(2,1)); result = bool(tc2 < tc1)"},
  {"claim":"Combined power of two lenses adds","code":"P1,P2=3,2; P=P1+P2; result = (P==5)"}
]