A thin, double-convex lens has a refractive index of
1.50. The radius of curvature of the front surface is
15 cm and that of the rear surface is 10 cm. See
sketch. (a) How far from the lens would an image of
the sun be formed? (b) How far from the lens would
an image of a toy figure 24 cm from the lens be
formed? (c) How do the answers to (a) and (b)
change if you flip the lens over?
�
To answer questions (a) and (b), we can use the lens maker's formula and the lens equation. The lens maker's formula relates the focal length (f) of a lens to the refractive index (n) and the radii of curvature of its two surfaces (R1 and R2). The lens equation relates the object distance (u), the image distance (v), and the focal length (f) of the lens.
The lens maker's formula is given by:
1/f = (n - 1) * ((1/R1) - (1/R2))
The lens equation is given by:
1/f = (1/v) - (1/u)
(a) To find the image distance when the object is the sun, we assume that the object is at infinity. So, the object distance (u) is infinite. Substituting u = ∞ in the lens equation, we have:
1/f = (1/v) - 0
1/f = 1/v
Since the object distance is infinite, the image distance (v) will be equal to the focal length (f).
(b) To find the image distance when the object is a toy figure 24 cm from the lens, we need to find the object distance (u) and then substitute it into the lens equation. Given the object distance (u) = 24 cm, we can calculate the image distance (v) using the lens equation.
(c) If you flip the lens over, the front surface becomes the rear surface and vice versa. This means that the radii of curvature of the surfaces change. In this case, you would need to recalculate the focal length, object distance, and image distance using the new radii of curvature and the lens maker's formula.
To summarize:
(a) The image distance for the sun would be equal to the focal length of the lens.
(b) To find the image distance for a toy figure, use the lens equation with the given object distance.
(c) If you flip the lens over, recalculate the focal length, object distance, and image distance using the new radii of curvature and the lens maker's formula.