Derive the following.
Combine these two expressions / equations to obtain an expression for focal length of the lens.
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Ray Optics and Optical Instruments - ISC Class 12 Physics Questions with Answers, Page 2
122 past-paper questions on Ray Optics and Optical Instruments from ISC Class 12 Physics papers (2027-2018), newest first, in full. Questions 21-40 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Answer the following.
Draw a labelled ray diagram of an image formed by this instrument, assuming
(a) a small upright object.
(b) image lies at least distance of distinct vision.
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Answer the following.
Why are reflecting telescopes preferred to refracting telescopes for astronomical observations?
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Answer the following.
A student studies details of a microorganism with the help of an instrument. Name the instrument used by him.
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Answer the following.
Give any one example where a ray of light travelling from one optical medium to another travels undeviated.
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Solve the following.
A bi-convex lens of focal length $f_{1}$ is placed in air as shown in Figure 3(a) below.
The radii of curvature of its first and second surfaces are R and 2R respectively. The lens is cut along the plane CD. Compare the focal length $f_{2}$ of the resulting lens shown in Figure 3(b) with that of the original lens shown in Figure 3(a).
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Answer
AIUsing the Lens Maker's Formula:
$\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_{1}} - \frac{1}{R_{2}}\right)$
For the original bi-convex lens (Figure 3(a)):
$R_{1} = +R$ and $R_{2} = -2R$
$\frac{1}{f_{1}} = (\mu - 1)\left(\frac{1}{R} - \left(-\frac{1}{2R}\right)\right) = (\mu - 1)\frac{3}{2R}$
$f_{1} = \frac{2R}{3(\mu - 1)}$
For the cut lens (Figure 3(b)):
The first surface is plane ($R_{1}' = \infty$) and the second surface has radius $R_{2}' = -2R$:
$\frac{1}{f_{2}} = (\mu - 1)\left(\frac{1}{\infty} - \left(-\frac{1}{2R}\right)\right) = (\mu - 1)\frac{1}{2R}$
$f_{2} = \frac{2R}{\mu - 1}$
Comparing the focal lengths:
$\frac{f_{2}}{f_{1}} = \frac{\frac{2R}{\mu - 1}}{\frac{2R}{3(\mu - 1)}} = 3 \implies f_{2} = 3f_{1}$
Final answer: 3
Draw the following.
Draw a labelled diagram of an astronomical telescope when its final image lies at infinity.
Draw: ray diagram of an astronomical telescope when its final image lies at infinity (normal adjustment)
Must show: objective lens, eyepiece, parallel rays from distant object, intermediate real, inverted image at focus Fo and Fe, parallel rays emerging from eyepiece
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Answer
AIA labelled ray diagram of an astronomical telescope in normal adjustment consists of a large-aperture, long-focal-length objective lens and a smaller eyepiece separated by $L = f_o + f_e$. Parallel rays from a distant object enter the objective at angle $\alpha$ and form a real, inverted, diminished intermediate image $A'B'$ at the common focal plane ($F_o$ coincides with $F_e$). The rays then refract through the eyepiece and emerge as parallel rays entering the observer's eye at angle $\beta$, forming the final inverted image at infinity.
Answer the following.
Consider two thin lenses, M and N having focal lengths of $f_{1}$ and $f_{2}$, respectively. They are kept in contact with each other as shown in Figure 6 below. A point object 'S' is kept on the common principal axis. The first lens M forms an image at $I_{1}$, which serves as a virtual object for the second lens N. The final image formed by the combination is 'I'.
(i)[2.0]
Apply the lens formula for the formation of:
(a) Image $I_{1}$ by the first lens M.
(b) Image I by the second lens N.
(ii)[1.0]
Hence, obtain an expression for equivalent focal length (F) in terms of $f_{1}$ and $f_{2}$.
To show: $\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
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Answer in one word.
The image below shows a compound microscope. Which one of the two lenses $L_{1}$ or $L_{2}$ has a larger focal length?
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Answer
AILens $L_1$ has a larger focal length.
In a compound microscope, $L_1$ is the eyepiece and $L_2$ is the objective. The eyepiece has a larger focal length (and larger aperture) than the objective lens ($f_e > f_o$) to provide appropriate magnification and a comfortable field of view.
Answer the following.
Draw a labelled ray diagram of an image formed by this instrument, assuming:
(a) a small upright object.
(b) image lies at least distance of distinct vision.
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Answer the following.
A virologist studies details of a virus with the help of an instrument. Name the instrument used by him.
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Solve the following.
Two convex lenses having focal length of $1.5\text{ cm}$ and $5\text{ cm}$ are placed coaxially to form a compound microscope. When a pin is kept at a distance of $1.6\text{ cm}$ from the objective lens, a virtual magnified image is formed at a distance of $25\text{ cm}$ from the eyepiece. Calculate the length of the microscope.
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Answer the following.
figure 1
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Answer the following.
What is the focal length of $L_1$?
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Answer the following.
Name the type of mirror used here.
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Answer the following.
How should Student 2 adjust the screen to obtain an accurate reading?
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Answer the following.
What is the focal length of the given lens?
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Solve the following.
Two identical thin convex lenses, each having an optical power of $2\text{ D}$ are kept in contact with each other. Calculate focal length of the combination.
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Draw the following.
Figure 3 below shows an optical pin kept in front of a lens mirror combination. It is found that the final image formed by the lens mirror combination coincides with the object pin.
Draw the ray diagram showing the formation of the final image (I).
Draw: ray diagram showing the formation of the final image (I)
Must show: formation of the final image (I), optical pin, lens mirror combination
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Answer the following.
How is the refractive index of the material of a prism dependent on the angle of incidence?
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