Category: Part 5: Optics

Problem Statement A glass lens with refractive index $n = 1.5$ has radii of curvature $R_1 = 20\,\text{cm}$ and $R_2 = -30\,\text{cm}$. Find the focal length in air. Given Information $R_1 = 20\,\text{cm}$ Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws…

Problem Statement Solve the optics problem: A converging lens forms a real image of magnification $|m| = 2$ on a screen. The distance between object and screen is $L = 90$ cm. Find the focal length. For a real inverted image, $m = -2$ so $v = 2|u|$. With $u$ negative: $|u|+v = L$, so…

Problem Statement Solve the optics problem: Two lenses $f_1 = 20$ cm and $f_2 = -30$ cm in contact. Find combined focal length and power. $$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}\;\Rightarrow\;\boxed{f=60\text{ cm}}$$ $$P = P_1+P_2 = 5\text{ D}-3.33\text{ D} = \boxed{1.67\text{ D}}$$ Given Information $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}\;\Rightarrow\;\boxed{f=60\text{ cm}$ $P = P_1+P_2 = 5\text{ D}$ Physical Concepts & Formulas This problem applies fundamental…

Problem Statement Solve the rotational mechanics problem: Magnifying glass $f = 5$ cm, near point $d_0 = 25$ cm. Find angular magnification for image at infinity. Object placed at focal plane; unaided angle $\alpha_0 = h/d_0$, aided angle $\alpha = h/f$. $$M = \frac{d_0}{f} = \frac{25}{5} = \boxed{5\times}$$ Given Information See problem statement for all…

Problem Statement Solve the optics problem: Object at $u = 30$ cm from a converging lens $f = 20$ cm. Find image position and magnification. $$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\;\Rightarrow\;\frac{1}{v}=\frac{1}{20}+\frac{1}{-30}=\frac{1}{60}\;\Rightarrow\; v=60\text{ cm}$$ $$m = v/u = 60/(-30) = -2$$ Real, inverted image, magnified $\times Given Information $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\;\Rightarrow\;\frac{1}{v}=\frac{1}{20}+\frac{1}{-30}=\frac{1}{60}\;\Rightarrow\; v=60\text{ cm}$ $m = v/u = 60/$ Physical Concepts & Formulas This…

Problem Statement Solve the kinematics problem: A beam strikes a glass plate ($h = 2.0$ cm, $n = 1.7$) at $\theta = 45°$. Find the perpendicular displacement of the transmitted beam. $$\sin r = \sin 45°/1.7 = 0.416 \implies r = 24.6°$$ $$d = \frac{h\sin(\theta-r)}{\cos r} = \frac{2.0\sin 20.4°}{\cos 24.6°} = \frac{2.0 \times 0.348}{0.909} \approx…

Problem Statement Solve the optics problem: Object at $u = 15$ cm from a concave mirror of focal length $f = 10$ cm. Find image position and magnification. Mirror equation ($u = -15$ cm, $f = -10$ cm, real-is-negative convention): $$\frac{1}{v}+\frac{1}{u}=\frac{1}{f} \implies \frac{1}{v}=-\frac{1}{10}+\frac{1}{15}=-\frac{1}{30} \implies v=-3 Given Information See problem statement for all given quantities. Physical…

Problem Statement A point source is at the bottom of a water-filled vessel, depth $h = 80$ cm, $n = 1.33$. Find the area of the illuminated circle at the surface. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement A ray passes through a glass prism (refracting angle $\Theta = 60°$, $n = 1.5$) symmetrically. Find the angle of minimum deviation. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws…

Problem Statement A ray hits a prism face at the critical angle $\theta_c$ for the glass–air interface. Prism angle $\Theta = 30°$, $n = 1.5$. Find the deviation of the emergent ray. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…