Questions: Ray Optics And Optical Instruments

Q1. State the Cartesian sign convention used for spherical mirrors.

Answer (English): All lengths in mirror problems start at the pole. A length measured along the incoming light earns a plus sign, one measured the other way earns a minus sign. Heights measured above the principal axis are positive and heights below it are negative. With this convention a concave mirror has a negative focal length and a convex mirror has a positive focal length.

Hinglish: Distances pole se naapo, incident light ki direction me positive aur ulti negative. Axis ke upar height positive, neeche negative. Concave mirror ka f negative aur convex ka positive hota hai.

Q2. Why does a convex mirror always form a virtual and diminished image?

Answer (English): A convex mirror diverges the reflected rays. The reflected rays appear to come from a focus behind the mirror, so the image is virtual. The image always lies between the pole and the focus, behind the mirror, so it is smaller than the object for every object position.

Hinglish: Convex mirror rays ko diverge karta hai, isliye image virtual banti hai. Image pole aur focus ke beech mirror ke peeche hoti hai, isliye hamesha chhoti hoti hai.

Q3. Define the critical angle for total internal reflection.

Answer (English): The critical angle is the angle of incidence in the denser medium for which the refracted ray grazes the surface, with an angle of refraction of 90 degrees. For incidence beyond this angle, no light is refracted and the ray is totally internally reflected. It is given by sine of the critical angle equal to the reciprocal of the refractive index when the rarer medium is air.

Hinglish: Critical angle wahan hota hai jahan refracted ray surface ke saath 90 degree par chali jaati hai. Isse zyada angle par total internal reflection hota hai. sin C = 1/n formula hai.

Q4. Why does a coin at the bottom of a beaker look raised when water is poured in?

Answer (English): The light from the coin bends away from the normal at the water-air surface, so the rays reaching the eye appear to come from a point above the actual coin. For near-normal viewing the apparent depth is the real depth divided by the refractive index of water, so the coin appears raised by real depth minus apparent depth.

Hinglish: Paani se aane wali rays surface par normal se door mudti hain, isliye eye ko coin upar dikhta hai. Apparent depth = real depth / n, isliye coin utha hua lagta hai.

Q5. Write the lens maker formula and explain each term.

Answer (English): The lens maker formula is one over f equals (n minus 1) times the difference between one over R1 and one over R2. In this relation f is the focal length inside the surrounding medium, n is the refractive index of the glass relative to that medium, and the two radii carry signs set by the cartesian rule. For use in a liquid the relative refractive index replaces n.

Hinglish: Formula: 1/f = (n - 1)(1/R1 - 1/R2). f focal length, n material ka refractive index surrounding medium ke respect me, R1 aur R2 surfaces ke radii. Liquid me relative refractive index lagao.

Q6. A converging lens has focal length 40 cm. Express its power in dioptres.

Answer (English): Dioptre power is computed as one divided by the focal length written in metres. Converting 40 cm to 0.40 m gives a power of 2.5 dioptres, and the plus sign marks a converging element.

Hinglish: Power = 1/f (metres me). 40 cm = 0.40 m, isliye P = 1/0.40 = +2.5 D. Positive sign ka matlab converging lens.

Q7. Why is total internal reflection used in an optical fibre?

Answer (English): The core of the fibre is optically denser than its cladding. A ray travelling almost along the fibre meets the boundary at a glancing angle that exceeds the critical angle. The boundary then reflects the ray instead of letting it refract out, and the same process repeats along the fibre, guiding the signal with very little loss.

Hinglish: Fibre ke core ka refractive index cladding se zyada hota hai. Andar chalti ray boundary par critical angle se bada angle banati hai, isliye bahar refract hone ke bajaye reflect hoti hai aur signal aage chalta jaata hai.

Q8. State the prism formula at minimum deviation.

Answer (English): At minimum deviation the ray inside the prism is parallel to the base, the angle of incidence equals the angle of emergence, and the deviation is smallest. Then the refractive index equals sine of (A plus delta minimum) divided by 2, divided by sine of A divided by 2, where A is the refracting angle.

Hinglish: Minimum deviation par ray base ke parallel hoti hai aur i = e hota hai. Tab n = sin((A+delta_m)/2) / sin(A/2) formula lagta hai.

Q9. How does a compound microscope produce a large magnification?

Answer (English): The objective has a very short focal length and forms a real, inverted and magnified image of the object inside the focal length of the eyepiece. The eyepiece then works as a simple magnifier and produces a further magnified virtual image. The total magnification is the product of the objective and eyepiece magnifications, so a small objective focal length gives a large magnification.

Hinglish: Microscope me objective chhote focal length se real magnified image banata hai, phir eyepiece usko magnify karta hai. Total magnification dono ka product hota hai, isliye objective ka chhota f bada magnification deta hai.

Q10. Why is a reflecting telescope preferred over a refracting telescope?

Answer (English): A reflecting telescope uses a concave mirror instead of an objective lens, so it has no chromatic aberration. A mirror can also be made much larger than a lens without sagging problems, which gives a larger aperture, better light gathering and better resolving power.

Hinglish: Reflecting telescope me mirror hota hai, isliye chromatic aberration nahi hota, aur mirror lens se zyada bada ban sakta hai. Isse light gathering aur resolving power behtar hoti hai.

Marks pattern for this chapter

One-mark items check the sign convention, the focal length of a mirror from its radius, or one relation such as the power of a lens. Two and three mark items ask for an image position, a critical angle or a numerical from the lens maker formula. Five-mark items combine a prism calculation with reasoning, or ask for the full working of an optical instrument. Writing the formula, the substituted values with signs, and the final statement of the image type covers all of them.

Quiz below: five multiple choice questions on mirror signs, the lens maker formula, total internal reflection, the prism formula and telescope magnification. Attempt them after revising the formula sheet and the three topic pages.