Geometrical Optics and Image Formation (4D) - Chem & Physics

1. State the lateral magnification equation for a thin lens or spherical mirror.

   $m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}$. Magnification expresses the ratio of image to object height, with sign denoting orientation.

2. What does a negative image distance $d_i<0$ indicate under the standard sign convention?

   Virtual image (same side as object). Negative image distance indicates a virtual image where rays appear to diverge from the object side.

3. State the focal length and radius of curvature relationship for a spherical mirror.

   $f=\frac{R}{2}$. For spherical mirrors, focal length equals half the radius of curvature.

4. What type of image is formed by a plane mirror (real or virtual, upright or inverted)?

   Virtual, upright, same size. Plane mirrors reflect rays to form an apparent image behind the surface without inversion or size change.

5. For a converging lens, what image type occurs when $d_o>2f$?

   Real, inverted, reduced; image between $f$ and $2f$. Object beyond twice focal length forms reduced real image between focal point and center of curvature.

6. Find $d_i$ for a lens with $f=10\,\text{cm}$ and $d_o=30\,\text{cm}$ using $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$.

   $d_i=15\,\text{cm}$. Thin lens equation yields positive image distance for converging lens with object beyond focal point.

7. Find magnification $m$ if $d_o=30\,\text{cm}$ and $d_i=15\,\text{cm}$ for a thin lens.

   $m=-\frac{1}{2}$. Magnification formula gives negative value for inverted real images.

8. What does a positive image distance $d_i>0$ indicate under the standard sign convention?

   Real image (formed on outgoing-light side). Positive image distance denotes a real image where rays converge on the opposite side.

9. What is the refractive index formula in terms of light speeds in vacuum and medium?

   $n=\frac{c}{v}$. Refractive index quantifies the reduction in light speed from vacuum $c$ to medium $v$.

10. What is the critical angle formula for light going from $n_1$ to lower index $n_2$?

    $\theta_c=\sin^{-1}\!\left(\frac{n_2}{n_1}\right)$ for $n_1>n_2$. Critical angle is derived from Snell's law when the refracted angle reaches 90 degrees for $n_1 > n_2$.

11. Which lens always produces a virtual, upright, reduced image for a real object?

    Diverging (concave) lens. Diverging lenses produce diminished virtual images on the object side for real objects.

12. State the thin lens equation relating focal length, object distance, and image distance.

    $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$. Thin lens equation links focal length to object and image distances for image formation.

13. For a converging lens, what image type occurs when $f<d_o<2f$?

    Real, inverted, magnified; image beyond $2f$. Object between focal length and twice focal forms enlarged real image beyond twice focal.

14. Identify the refracted direction: light goes from $n_1=1.0$ to $n_2=1.5$; does it bend toward or away from the normal?

    Toward the normal. Entering higher refractive index slows light, causing bending toward the normal per Snell's law.

15. Find $d_i$ for a diverging lens with $f=-20\,\text{cm}$ and $d_o=40\,\text{cm}$.

    $d_i=-\frac{40}{3}\,\text{cm}$. Negative focal length in equation produces negative image distance for virtual image.

16. Identify the sign of focal length $f$ for a diverging (concave) thin lens.

    $f<0$. Diverging lenses spread parallel rays, assigned negative focal length in sign convention.

17. Identify the sign of focal length $f$ for a converging (convex) thin lens.

    $f>0$. Converging lenses focus parallel rays to a point, assigned positive focal length in convention.

18. Find the critical angle for $n_1=1.50$ (inside) to $n_2=1.00$ (air).

    $\theta_c\approx41.8^\circ$. Formula computes angle where refraction gives 90 degrees, using inverse sine of index ratio.

19. What is the law of reflection for a ray striking a mirror?

    $\theta_i=\theta_r$. Law of reflection equates the angles of incidence and reflection measured from the normal.

20. What does a negative magnification $m<0$ indicate about image orientation?

    Inverted image. Negative magnification signifies that the image is upside down relative to the object.

21. State the plane mirror relationship between image distance and object distance.

    $d_i=-d_o$. In plane mirrors, image appears equidistant behind as object is in front, yielding negative distance.

22. For a converging lens, what image type occurs when $d_o<f$?

    Virtual, upright, magnified; image on object side. Object inside focal length results in enlarged virtual image on the same side.

23. Which mirror always produces a virtual, upright, reduced image for a real object?

    Convex mirror. Convex mirrors diverge rays, forming smaller virtual images regardless of object position.

24. Identify the condition for total internal reflection in terms of angle and indices.

    From $n_1>n_2$ with $\theta_1>\theta_c$. Total internal reflection requires incidence from higher index at an angle exceeding the critical angle.

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