Geometrical Optics flash cards

1. 1.State the laws of reflection.

   (1) The angle of incidence equals the angle of reflection ($i=r$). (2) The incident ray, reflected ray and normal at the point of incidence all lie in the same plane.

   Hint: Two rules: angles + coplanarity.

2. 2.What is the nature and size of the image formed by a plane mirror?

   Virtual, erect, laterally inverted, of the same size as the object, and located as far behind the mirror as the object is in front.

   Hint: Same size, equal distance behind.

3. 3.By what angle does a reflected ray rotate if the mirror is rotated by angle $\theta$ (incident ray fixed)?

   The reflected ray rotates by $2\theta$.

   Hint: Mirror turns $\theta$, ray turns double.

4. 4.How many images are formed by two plane mirrors inclined at angle $\theta$?

   $n=\dfrac{360}{\theta}-1$ when $\dfrac{360}{\theta}$ is even; for odd, $n=\dfrac{360}{\theta}-1$ if the object is off the bisector, or $\dfrac{360}{\theta}$ if it is not an integer, take the nearest.

   Hint: $360/\theta$ then adjust.

5. 5.Distinguish between a concave and a convex mirror.

   A concave mirror is a converging mirror (reflecting surface caves inward). A convex mirror is a diverging mirror (reflecting surface bulges outward).

   Hint: Concave converges.

6. 6.What is the relation between focal length $f$ and radius of curvature $R$ of a spherical mirror?

   $f=\dfrac{R}{2}$; the focal length is half the radius of curvature.

   Hint: Focus is midway to centre.

7. 7.State the mirror formula.

   $\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$, where $u$ is object distance, $v$ image distance, $f$ focal length.

   Hint: $1/v+1/u=1/f$.

8. 8.Define linear (transverse) magnification for a mirror.

   $m=\dfrac{h'}{h}=-\dfrac{v}{u}$, ratio of image height to object height.

   Hint: $m=-v/u$.

9. 9.State the sign convention (Cartesian) used for mirrors and lenses.

   Distances are measured from the pole/optical centre; those measured along the incident light direction are positive, opposite are negative. Heights above the axis are positive, below negative.

   Hint: Incident direction positive.

10. 10.For a concave mirror, what does a negative magnification indicate?

    A real, inverted image (image on the same side as the object).

    Hint: Negative $m$ → real & inverted.

11. 11.What is the sign of $f$ for concave and convex mirrors?

    Concave mirror: $f$ negative. Convex mirror: $f$ positive (in the standard sign convention).

    Hint: Concave $f<0$.

12. 12.Where must an object be placed before a concave mirror to get a magnified real image?

    Between the focus $F$ and centre of curvature $C$; the image forms beyond $C$, real, inverted and enlarged.

    Hint: Between F and C.

13. 13.What kind of image does a convex mirror always form?

    A virtual, erect, diminished image located between the pole and focus, for all real object positions.

    Hint: Always virtual, erect, small.

14. 14.Why are convex mirrors used as rear-view mirrors in vehicles?

    They always form erect, diminished virtual images and provide a wider field of view.

    Hint: Wide view, erect small image.

15. 15.Where is the image formed when an object is at the centre of curvature of a concave mirror?

    At $C$ itself; the image is real, inverted and of the same size as the object ($m=-1$).

    Hint: Object at C → image at C, same size.

16. 16.Define refraction of light.

    The bending of light as it passes from one transparent medium to another due to a change in its speed.

    Hint: Speed change bends light.

17. 17.State Snell's law of refraction.

    $n_1\sin i=n_2\sin r$, or $\dfrac{\sin i}{\sin r}=\dfrac{n_2}{n_1}={}_1n_2$ (constant for a given pair of media).

    Hint: $n_1\sin i=n_2\sin r$.

18. 18.Define absolute refractive index of a medium.

    $n=\dfrac{c}{v}$, the ratio of the speed of light in vacuum to its speed in the medium.

    Hint: $n=c/v$.

19. 19.How does refractive index relate to wavelength when light enters a denser medium?

    Frequency stays constant; speed and wavelength decrease. $n=\dfrac{\lambda_{vac}}{\lambda_{med}}$.

    Hint: $\lambda$ shrinks, $f$ fixed.

20. 20.What is lateral shift in refraction through a glass slab?

    The perpendicular displacement between the incident ray direction and the emergent ray; the emergent ray is parallel to the incident ray but laterally displaced.

    Hint: Parallel emergent ray, sideways shift.

21. 21.Why does the emergent ray from a parallel-sided glass slab stay parallel to the incident ray?

    The refractions at the two parallel faces are equal and opposite, so the net angular deviation is zero (only a lateral shift remains).

    Hint: Equal & opposite bends cancel.

22. 22.Why does a pool of water appear shallower than it really is?

    Because of refraction; real depth and apparent depth are related by $n=\dfrac{\text{real depth}}{\text{apparent depth}}$.

    Hint: Apparent depth = real/n.

23. 23.Define critical angle.

    The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is $90^\circ$.

    Hint: Refraction just grazes at $90^\circ$.

24. 24.Relate critical angle $C$ to refractive index.

    $n=\dfrac{1}{\sin C}$ (for a denser medium of index $n$ against vacuum/air).

    Hint: $\sin C=1/n$.

25. 25.State the two conditions necessary for total internal reflection.

    (1) Light must travel from a denser to a rarer medium. (2) The angle of incidence must exceed the critical angle.

    Hint: Denser→rarer and $i>C$.

26. 26.Give two natural/technological examples of total internal reflection.

    Mirage, sparkle of diamonds, optical fibres, totally reflecting prisms in binoculars/periscopes.

    Hint: Mirage, diamond, optical fibre.

27. 27.Why does a diamond sparkle brilliantly?

    Its very high refractive index gives a small critical angle ($\approx 24.4^\circ$), so light undergoes repeated total internal reflection before emerging.

    Hint: High n, small critical angle.

28. 28.How does an optical fibre guide light?

    By repeated total internal reflection at the core–cladding boundary, the core having a higher refractive index than the cladding.

    Hint: TIR down the core.

29. 29.Why is a mirage seen on hot roads?

    Hot air near the ground is less dense (lower n); light from the sky bends and undergoes total internal reflection, creating an inverted watery image.

    Hint: TIR in hot rarer air.

30. 30.State the equation for refraction at a single spherical surface.

    $\dfrac{n_2}{v}-\dfrac{n_1}{u}=\dfrac{n_2-n_1}{R}$, where light travels from medium $n_1$ into $n_2$.

    Hint: $n_2/v - n_1/u = (n_2-n_1)/R$.

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