An innovative optical sensor system for a miniature drone incorporates a combination of various…
An innovative optical sensor system for a miniature drone incorporates a combination of various optical elements. A beam of light from an LED source first passes through a convex spherical refracting surface (radius of curvature R = 20 cm) separating air $\mu_1 = 1\cdot0$ from a glass medium of refractive index $\mu_2 = 1\cdot5$. The light then enters a thin biconvex lens of focal length 10 cm. Finally, the beam strikes a concave spherical mirror of radius of curvature 30 cm, which acts as a collector, focusing the rays onto a photodetector (optical instrument application) to measure light intensity.
(i)[1.0]
If the drone operates in a highly humid or misty environment where a film of water completely coats the lens surfaces, how will the refractive power of this lens change?
(ii)[2.0]
A point object is placed in air at a distance of 60 cm in front of the convex spherical refracting surface. What is the position of the image formed by this surface?
(iii)[1.0]
If this setup is to be modified to function as a reflecting astronomical telescope, what roles would be played by the mirror and the lens?
(iv)[1.0]
Which mirror collects light from a distant object most efficiently?
Answer
Answer (i)
AIWritten by AI (gemini) - it can contain mistakes.
The refractive power of the lens will decrease (its focal length will increase), because the relative refractive index $\frac{\mu_g}{\mu_w} = \frac{1\cdot5}{1\cdot33} \approx 1\cdot128$ is smaller than in air ($\mu_g = 1\cdot5$).
Answer (ii)
AIWritten by AI (gemini) - it can contain mistakes.
Refraction at spherical surface: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.
Given $\mu_1 = 1\cdot0$, $\mu_2 = 1\cdot5$, $u = -60\text{ cm}$, $R = +20\text{ cm}$.
$\frac{1\cdot5}{v} - \frac{1\cdot0}{-60} = \frac{1\cdot5 - 1\cdot0}{20} \implies \frac{1\cdot5}{v} + \frac{1}{60} = \frac{0\cdot5}{20} = \frac{1}{40}$.
$\frac{1\cdot5}{v} = \frac{1}{40} - \frac{1}{60} = \frac{3-2}{120} = \frac{1}{120} \implies v = 1\cdot5 \times 120 = +180\text{ cm}$.
The image is formed at a distance of $180\text{ cm}$ inside the glass medium (to the right of the surface).
Final answer: 180 cm
Answer (iii)
AIWritten by AI (gemini) - it can contain mistakes.
Concave spherical mirror acts as the objective (to collect and focus light from distant objects), and the thin biconvex lens acts as the eyepiece (to magnify the focused image).
Answer (iv)
AIWritten by AI (gemini) - it can contain mistakes.
A parabolic mirror (it eliminates spherical aberration and focuses all parallel rays to a sharp focus).
From ISC 2027 Specimen Physics Paper 1, question 20.