A person with a normal near point (25 cm) using a compound microscope with objective of focal length 8.0 mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope,

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall ((3))m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam ((12))cm from P. At what point does the beam converge if the lens is a concave lens of focal length ((16))cm?

A small telescope has an objective lens of focal length ((140))cm and an eyepiece of focal length ((5.0))cm. What is the magnifying power of the telescope for viewing distant objects when the final image is formed at the least distance of distinct vision (((25))cm)?

Answer the following questions: (d) Why must both the objective and the eyepiece of a compound microscope have short focal lengths?

A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

A small telescope has an objective lens of focal length 144cm and an eyepiece of focal length 6.0cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?

A card sheet divided into squares each of size ((1 \text{ mm}^{2})) is being viewed at a distance of ((9)) cm through a magnifying glass (a converging lens of focal length ((9)) cm) held close to the eye. What is the angular magnification (magnifying power) of the lens?

A small telescope has an objective lens of focal length ((144))cm and an eyepiece of focal length ((6.0))cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?

Answer the following questions: The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?

What is the height of the final image of the tower if it is formed at 25cm?

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

A screen is placed ((90))cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by ((20))cm. Determine the focal length of the lens.

A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15cm. How far from the objective should an object be placed in order to obtain the final image at (b) at infinity? What is the magnifying power of the microscope in each case?

A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

Answer the following questions: In viewing through a magnifying glass, one usually positions one’s eyes very close to the lens. Does angular magnification change if the eye is moved back?

At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.

An object of size ((3.0))cm is placed ((14))cm in front of a concave lens of focal length ((21))cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

At what angle should a ray of light be incident on the face of a prism of refracting angle ((60^{\circ})) so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is ((1.524)).