Ray Optics and Optical Instruments Set-1

Q1. A compound microscope has an objective of focal length $f_o=8\,\text{mm}$ and an eyepiece of focal length $f_e=20\,\text{mm}$. The tube length (distance between the focal points of objective and eyepiece) is $L=160\,\text{mm}$. When adjusted for a relaxed eye (final image at infinity) the approximate total magnification (use $M=\dfrac{L}{f_o}\cdot\dfrac{25}{f_e}$ with $25\,\text{cm}=250\,\text{mm}$) is:

Q2. Assertion (A): A thin glass lens immersed in a liquid whose refractive index equals that of the glass behaves as if it has infinite focal length.
Reason (R): In that medium the lens surfaces become optically flat so they cannot refract light.

Q3. In an experiment with a thin lens, the plot of $1/v$ (in $\text{m}^{-1}$) versus $1/u$ (in $\text{m}^{-1}$) is a straight line whose $y$–intercept equals $0.25\ \text{m}^{-1}$. Using the thin lens relation $1/u+1/v=1/f$, the focal length $f$ of the lens is approximately:

Q4. A thin convex lens of focal length $f=10\,\text{cm}$ is fixed. An object is placed at $u=30\,\text{cm}$ to the left of the lens. A plane mirror is placed on the right of the lens at $20\,\text{cm}$ from the lens. Light from the object goes through the lens, reflects from the plane mirror and returns through the lens. Neglect lens thickness and paraxial approximation. The final image after the second pass through the lens is formed approximately at:

Q5. Two stars have an angular separation of $1''$ (one arcsecond). Using the Rayleigh criterion for a circular aperture $\theta_{\min}=1.22\lambda/D$ and $\lambda=550\ \text{nm}$, the minimum objective diameter $D$ required to just resolve them is approximately:

Q6. Assertion (A): Stopping down (reducing) the aperture of a lens reduces spherical aberration in the image.
Reason (R): Spherical aberration is produced mainly by marginal rays; reducing the aperture blocks marginal rays leaving predominantly paraxial rays that suffer much less deviation.

Q7. Two thin lenses of focal lengths $f_1=+10\,\text{cm}$ and $f_2=+20\,\text{cm}$ are placed coaxially with their centers separated by $d=5\,\text{cm}$. The effective focal length $F$ of the two-lens system (thin-lens formula for separated lenses) is given by $\dfrac{1}{F}=\dfrac{1}{f_1}+\dfrac{1}{f_2}-\dfrac{d}{f_1f_2}$. The equivalent focal length $F$ is:

Q8. In an experiment with a thin convex lens a plot of lateral magnification $m=-v/u$ versus object distance $u$ shows that $m=-1$ when $u=30\,\text{cm}$. Using the thin lens relations, the focal length $f$ of the lens is:

Q9. Assertion (A): A simple astronomical refracting telescope produces an inverted image of distant objects.
Reason (R): The eyepiece flips the image produced by the objective, causing the inversion.

Q10. In the lens-displacement method the distance between a fixed object and its screen is $D=60\,\text{cm}$. Two lens positions separated by $L=20\,\text{cm}$ produce sharp images on the screen. Using the relation $f=\dfrac{D^2-L^2}{4D}$, the focal length $f$ of the lens is approximately: