If an object 5cm high is placed at a distance of 12cm from a concave mirror of focal length 8cm, find the position, nature and height of the image formed.
Answers
Answer:
its position will be 24cm.
nature will be virtual and erect,
height will be 10cm
Explanation:
see the attachment
Answer
Image distance (v) = -24cm, Height of image (h') = -10cm and nature of image is real, inverted and enlarged.
Explanation
Given that, height of object is 5 cm and is put at a distance of 12 cm from concave mirror.
→ h (height of object) = 5 cm, u (object distance) = -12 cm
Also, the focal length of concave mirror is 8 cm.
→ f (focal length) = - 8 cm
We have to find the position, nature and height of the image formed.
We know that, Mirror formula:
1/f = 1/v + 1/u
Substitute the known values
→ 1/(-8) = 1/v + 1/(-12)
→ -1/8 = 1/v - 1/12
→ -1/8 + 1/12 = 1/v
→ (-3 + 2)/24 = 1/v
→ -1/24 = 1/v
Cross-multiply them
→ v = - 24 cm
m = h'/h (height of image/height of object) = -v/u
→ h'/h = -v/u
Substitute the known values
→ h'/(5) = -(-24)/(-12)
→ h'/5 = -24/12
→ h'/5 = -2/1
Cross-multiply them
→ h' = 5(-2)
→ h' = - 10cm
Nature: Image formed is real, inverted and enlarged.