$A$ concave mirror of focal length $100 \ cm$ is used to obtain the image of the sun,which subtends an angle of $30'$. The diameter of the image of the sun will be.....$cm$.

The field of view is maximum for

An object and a concave mirror of focal length $f=10 \text{ cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15 \text{ cm s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \text{ cm}$,the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame,and the object forms a real image. The magnitude of $V_m$ is . . . . . $\text{cm s}^{-1}$.

Assertion : $A$ point object is placed at a distance of $26 \ cm$ from a convex mirror of focal length $26 \ cm$. The image will not form at infinity.
Reason : For the above-given system,the equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ gives $v = \infty$.

When an object is placed at a distance of $25 \; cm$ from a mirror,the magnification is $m_1$. The object is moved $15 \; cm$ away with respect to the earlier position,magnification becomes $m_2$. If $\frac{m_1}{m_2} = 4$,the focal length of the mirror is: (in $; cm$)

Let the transverse magnification produced by a spherical mirror be $m$. Then,for the same position of the object,the longitudinal magnification will be: