$A$ student measures the focal length of a convex lens by obtaining an image of an object pin at a distance '$v$' from the lens,where the object pin is at a distance '$u$' from the lens. What will the graph between '$u$' and '$v$' look like?

Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of $10000 \, cd$ at a distance of $0.3 \, m$. The distance between the sun and the earth is $1.5 \times 10^{11} \, m$.

$A$ prism with a refractive index of $1.5$ and an angle $A = 4^o$ is placed in front of a mirror. When the incident ray is reflected by the mirror,what is the total deviation in degrees?

An optical arrangement consists of two concave mirrors $M_1$ and $M_2$,and a convex lens $L$ with a common principal axis,as shown in the figure. The focal length of $L$ is $10 \text{ cm}$. The radii of curvature of $M_1$ and $M_2$ are $20 \text{ cm}$ and $24 \text{ cm}$,respectively. The distance between $L$ and $M_2$ is $20 \text{ cm}$. $A$ point object $S$ is placed at the mid-point between $L$ and $M_2$ on the axis. When the distance between $L$ and $M_1$ is $n/7 \text{ cm}$,one of the images coincides with $S$. The value of $n$ is. . . .

In a grease spot photometer,light from a lamp with a dirty chimney is exactly balanced by a point source at a distance of $10 \, cm$ from the grease spot. On cleaning the chimney,the point source is moved by $2 \, cm$ to obtain balance again. The percentage of light absorbed by the dirty chimney is nearly......$\%$

$A$ wire is bent in the shape of a right-angled triangle and is placed in front of a concave mirror of focal length $f$,as shown in the figure. Which of the figures shown in the four options qualitatively represent$(s)$ the shape of the image of the bent wire? (These figures are not to scale.)