(a) (i) Cassegrain Reflecting Telescope
Ray Diagram Description: A large concave parabolic mirror (objective) collects parallel rays from a distant object. Before the rays converge at the focus, a small convex secondary mirror reflects them through a hole in the center of the objective, where an eyepiece magnifies the image.
Advantages:
- No Chromatic Aberration: Since mirrors are used instead of lenses, there is no dispersion of light.
- Mechanical Support: The objective mirror is heavy and can be supported from the back, unlike lenses which must be supported at the edges.
(a) (ii) Numerical Solution
Step 1 (Formula & Given Data): [1 Mark]
Given: $f_o = 50 f_e$. For normal adjustment (image at infinity), the length of the tube $L = f_o + f_e$.
Step 2 (Step-by-Step Mathematical Working): [1 Mark]
$$L = f_o + f_e$$ $$102 = 50 f_e + f_e$$ $$102 = 51 f_e$$ $$f_e = \frac{102}{51} = 2 \text{ cm}$$ $$f_o = 50 \times 2 = 100 \text{ cm}$$Step 3 (Final Concluded Answer): [0.5 Mark]
The focal length of the objective is $100 \text{ cm}$ and the eyepiece is $2 \text{ cm}$.
(b) (ii) Power of Combination Lens
Step 1 (Formula & Governing Law): [1 Mark]
Using the Lens Maker's Formula: $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.
For planoconcave lens ($f_1$): $R_1 = \infty, R_2 = +R$. So, $\frac{1}{f_1} = (n_1 - 1) \left( \frac{1}{\infty} - \frac{1}{R} \right) = -\frac{(n_1 - 1)}{R}$.
For equiconvex lens ($f_2$): $R_1 = R, R_2 = -R$. So, $\frac{1}{f_2} = (n_2 - 1) \left( \frac{1}{R} - \frac{1}{-R} \right) = \frac{2(n_2 - 1)}{R}$.
Step 2 (Step-by-Step Mathematical Working): [1 Mark]
Power of combination $P = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2}$
$$P = -\frac{(n_1 - 1)}{R} + \frac{2(n_2 - 1)}{R}$$ $$P = \frac{-n_1 + 1 + 2n_2 - 2}{R}$$Step 3 (Final Concluded Answer): [0.5 Mark]
$$P = \frac{2n_2 - n_1 - 1}{R}$$💡 EL10 Concept Insight: Think of the