A car is moving on a straight road at a speed of \(50\) km/h and a truck is ahead of the car and has a large plane mirror fixed vertically on the back of the truck. The truck is running at a speed of \(70\) km/h. For a stationary observer standing between the car and the truck, what is the speed of the image of the car in the mirror?

1.	\(40\) km/h	2.	\(70\) km/h
3.	\(20\) km/h	4.	\(90\) km/h

A fish at a depth \(y\) inside the water is seeing a bird. The bird is at a height \(x\) above the water level. If the refractive index of water is \(\mu,\) then the apparent distance of bird as seen by the fish is:
1. \(x+\mu y\)
2. \(y+\mu x\)
3. \(x+\frac{y}{\mu}\)
4. \(y+\frac{x}{\mu}\)

The magnification of a compound microscope for the final image at the least distance of distinct vision is \(90\). The magnification of the objective lens is \(15\). The value of the focal length of the eyepiece will be: 
1. \(5\) cm
2. \(6\) cm
3. \(\dfrac{1}{6}\) cm
4. \(12\) cm

A concave lens forms the image of an object such that the distance between the object and image is \(10\) cm. If magnification of the image is \(\frac{1}{4},\) the focal length of the lens is:
1. \(-\frac{20}{3}~\text{cm}\)
2. \(\frac{20}{3}~\text{cm}\)
3. \(\frac{40}{9}~\text{cm}\)
4. \(-\frac{40}{9}~\text{cm}\)

A ray of light incident on a prism of angle \(A\) and refractive index \(\mu\) will not emerge out of the prism for any angle of incidence, if:
1. \(\mu>\sin \frac{A}{2}\)
2. \(\mu>\cos{A}\)
3. \(\mu<\frac{1}{\sin A}\)
4. \(\mu>\frac{1}{\sin \frac{A}{2}}\)

In normal adjustment, the angular magnification of an astronomical telescope is \(39\). If length of the tube is \(2\) m, then focal length of the objective and eyepiece are respectively: