Question

1. Answer the following questions on mirrors/lenses

a. A concave mirror (f1 = 14.8 cm) and a convex mirror (f2 = −5.90 cm) are facing each other and are separated by a distance of 34.0 cm. An object is placed between the mirrors and is 17.0 cm from each mirror. Consider the light from the object that reflects first from the concave mirror and then from the convex mirror. What is the distance of the image (di2) produced by the convex mirror?

b. A person stands 2.35 m away from the reflecting surface of a plane mirror. (i) What is the distance between the person and his or her image? (ii) What are the image characteristics? (Real vs. Virtual, Erect vs. Inverted, Magnified vs. Diminished)

c. A point source of light is submerged 2.90 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?

d. A convex (converging) lens produces a real, inverted image of an object that is magnified 2.90 times when the object is 23.0 cm from the lens. What is the focal length of the lens?

Answer 1

1]

a] f1 = 14.8 cm and f2 = - 5.9 cm

for the 1st reflection from the concave mirror,

1/f1 = 1/v + 1/u

1/14.8 = 1/v + 1/17

=> v = 114.36 cm

object distance for the convex lens is then,

u' = 114.36 - 34 = 80.36 cm

- 1/5.9 = 1/80.36 + 1/v'

=> v' = di2 = - 5.5 cm

this is the distance of image produced by the convex mirror.

b] Object distance = 2.35 m

since the mirror is planar, its focal length is infinity and so the distance between the person and his/her image is also 2.35 m.

The image is Erect, Virtual and magnified.

c] The maximum angle for which the light will leave the lake is the critical angle and here it is:

where refractive index of water is taken to be 1.33 and for air is 1.0.

so,

D = 2.9 m

=> r = 2.9tan48.75 = 3.3 m

this is the maximum radius that the circle traced out can have.

d] m = v/u = 2.9

=> v = 2.9u

here, u=23 cm

therefore, v = 66.7 cm

1/f = 1/v + 1/u

1/f = 1/66.7 + 1/23

=> f = 17.1 cm

this is the focal length of the convex lens.