A flower of height 4 cm is placed 40 cm from the pole of a concave mirror used in a botanical garden. The mirror has a focal length of 30 cm. Determine the distance and height of the image formed.120 cm and 10 cm respectively150 cm and 15 cm respectively150 cm and 12 cm respectively120 cm and 12 cm respectively

To solve this problem, we can use the mirror formula and the magnification formula.

The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

The magnification formula is m = -v/u = h'/h, where m is the magnification, h' is the height of the image, and h is the height of the object.

Given: f = -30 cm (The focal length of a concave mirror is taken as negative) u = -40 cm (The object distance for a concave mirror is taken as negative) h = 4 cm

First, let's find the image distance (v) using the mirror formula:

1/v = 1/f - 1/u 1/v = 1/(-30) - 1/(-40) 1/v = -1/30 + 1/40 1/v = -4/120 + 3/120 1/v = -1/120

So, v = -120 cm. The negative sign indicates that the image is formed on the same side as the light is coming from, which is the usual for a concave mirror.

Next, let's find the height of the image (h') using the magnification formula:

m = h'/h m = -v/u m = -(-120)/-40 m = -3

So, h' = m * h = -3 * 4 = -12 cm. The negative sign indicates that the image is inverted.

Therefore, the image is formed 120 cm from the mirror and the height of the image is 12 cm. The correct answer is "120 cm and 12 cm respectively".