Category: Part 5: Optics

Problem Statement An achromatic doublet is made of two prisms: flint ($\omega_1 = 0.040$) and crown ($\omega_2 = 0.025$). The combination gives a mean deviation of $\delta = 3°$. Find the refracting angles of each prism. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles…

Problem Statement Solve the optics problem: A plano-convex lens ($n = 1.5$, $R = 20$ cm, flat side silvered) acts as a mirror. Find the effective focal length of the system. For a silvered lens (lens + mirror + lens system), the equivalent power is: $$P_{eq} = P_{lens}+P_{mirror}+P_{lens} = 2P_{lens}+P_{mirror}$$ Lens power: $P_L = (n-1)/R…

Problem Statement Solve the work-energy problem: A glass prism ($n_D = 1.60$, $n_F = 1.61$, $n_C = 1.59$) has refracting angle $\Theta = 5°$ (small). Find the angular dispersion and dispersive power. For a thin prism, deviation $\delta = (n-1)\Theta$. Angular dispersion: $$\delta_F – \delta_C = (n_F – n_C)\Theta = (1.61-1.59)\times 5° = 0.02 \time…

Problem Statement Solve the optics problem: An object is in water ($n_1 = 1.33$) 30 cm from a convex glass surface ($n_2 = 1.5$) with radius $R = 10$ cm. Find the image position. Refraction at a single spherical surface: $$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$$ With $u = -30$ cm, $R = +10$ cm: $$\frac{1.5}{v}-\frac{1.33}{-30}=\frac{0 Given Information See problem…

Problem Statement A compound microscope has objective $f_o = 4$ mm and eyepiece $f_e = 25$ mm. The tube length (image distance from objective to front focal plane of eyepiece) is $\Delta = 150$ mm. Near point $d_0 = 250$ mm. Find the total magnification. Given Information See problem statement for all given quantities. Physical…

Problem Statement A coin lies at the bottom of a vessel filled with water to depth $h = 40$ cm ($n = 1.33$). What is the apparent depth of the coin when viewed from directly above? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles…

Problem Statement A refracting telescope has objective focal length $f_o = 100$ cm and eyepiece focal length $f_e = 5$ cm. Find: (a) angular magnification for distant object, (b) length of telescope tube. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario…

Problem Statement Solve the optics problem: A glass lens ($n_g = 1.6$) submerged in water ($n_w = 1.33$) has focal length $f_{air} = 20$ cm in air. Find its focal length in water. In air: $1/f_{air} = (n_g-1)(1/R_1-1/R_2)$. In water: $1/f_w = (n_g/n_w – 1)(1/R_1-1/R_2)$. $$\frac{f_{air}}{f_w} = \frac{n_g-1}{n_g/n_w – 1} = \frac{0.6}{1.6/1.33- Given Information See…

Problem Statement Solve the optics problem: Two thin lenses of focal lengths $f_1 = 30$ cm and $f_2 = 20$ cm are separated by $d = 10$ cm. Find the equivalent focal length of the system. $$\frac{1}{f} = \frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1 f_2} = \frac{1}{30}+\frac{1}{20}-\frac{10}{30\times20}$$ $$= \frac{2+3}{60}-\frac{10}{600} = \frac{5 Given Information See problem statement for all given quantities.…

Problem Statement Solve the optics problem: A converging lens of focal length $f = 15$ cm forms a virtual image magnified 3 times. Find the object distance. Virtual upright image: $m = +3$, so $v = 3u$ (both negative for real object on same side). Using sign convention $u $$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$$ With $v = 3u$ (same…