A concave mirror for face viewing has focal length of \(0.4~\text{m}\). The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is:
1. \(1.60~\text{m}\)
2. \(0.16~\text{m}\)
3. \(0.32~\text{m}\)
4. \(0.24~\text{m}\)

A concave mirror with a radius of curvature of \(40~\text{cm}\) is placed at the bottom of a glass container. Water is filled in the container to a depth of \(5~\text{cm}\) above the mirror. A small particle floats on the surface of the water. When an observer looks at the particle from directly above (from air), they see an image at a distance \(d\) below the water surface due to the combined effect of reflection from the mirror and refraction at the water-air interface. The value of \(d\) is: (refractive index of water \(=1.33\))

1. \(11.7~\text{cm}\)
2. \(6.7~\text{cm}\)
3. \(13.4~\text{cm}\)
4. \(8.8~\text{cm}\)

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)
       

When an object is kept at a distance of \(30~\text{cm}\) from a concave mirror, the image is formed at a distance of \(10~\text{cm}\) from the mirror. If the object is moved with a speed of \(9~\text{cms}^{-1}\), the speed (\(\text{in cms}^{-1}\)) with which image moves at that instant is:
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)

A short straight object of height \(100\) cm lies before the central axis of a spherical mirror whose focal length has an absolute value \(|f|=40~\text{cm}\). The image of the object produced by the mirror is of height \(25\) cm and has the same orientation as the object. One may conclude from the information: