Question

An object 1cm tall is placed at 4cm from a convex lens with a focal length of 6cm. A convex mirror with a focal length of 4cm is situated 10cm from the convex lens. A)Using the thin lens equation calculate the location of the image. B)Describe the image using three of the following words; virtual, real , smaller, bigger, non-inverted, inverted.

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Answer 1

Height of the object is, h₁ = 1 cm = 0.01 m

Distance of the object from the convex lens is, u = 4 cm = 0.04 m

Focal length of the lens is, f_l = 6 cm = 0.06 m

Focal length of the convex mirror is, f_m = 4 cm = 0.04 m

Distance between the convex lens and the convex mirror is, d = 10 cm = 0.1 m

A) Let v be the image distance for image formed by the convex lens in the absence of the mirror. The image so formed will act as the object for mirror. The image formed by this mirror will in turn act as object for the convex lens to form the final image. Using the thin lens formula, we can write,

Thus,

v = -12 cm

The image lies at a distance of 12 cm from the lens and is on the same side as the object. Also, the image is upright.

Since the mirror is at a distance of 10 cm from the lens on the other side of it, the distance between object for the mirror and pole of the mirror is, u = -22 cm

Hence, using mirror formula, we can write,

v = +3.38 cm

Thus, the image is at a distance of 3.38 cm from the pole of the mirror and is located on the other side of the mirror and is upright. This image acts as object for the lens to form the final image.

Object distance for the lens is, u = 13.38 cm

Using the thin lens equation, we can write,

v = +10.88 cm

The image is at a distance of 10.88 cm from the pole of the lens and is on the same side as the actual object.

B) Since the image distance is positive, the image is real and is smaller and inverted.