if an object 4 cm height is placed at a distance of 18 cm from concave mirror having focal length 12 cm.find the position, nature, and height of images
Answers
Explanation:
Given:-
Object height ,ho = 4cm
Object distance ,u = -18cm
Focal length ,f = -12 cm
To Find:-
Position , nature & height of images.
Solution:-
According to the Question
Firstly we calculate the image distance of the object using mirror formula
• 1/v + 1/u = 1/f
where,
v is the Image Position
u is the object distance
f is the focal length
Substitute the value we get
:\implies:⟹ 1/v = 1/f - 1/u
:\implies:⟹ 1/v = 1/-12 - 1/(-18)
:\implies:⟹ 1/v = -1/12 + 1/18
:\implies:⟹ 1/v = -3+2/36
:\implies:⟹ 1/v = -1/36
:\implies:⟹ v = -36 cm
Hence, the image formed is 36 cm from the mirror .
Now, calculating the magnification of the image
m = hi/ho = -v/u
Substitute the value we get
:\implies:⟹ hi/4 = -36/-18
:\implies:⟹ hi/4 = 36/18
:\implies:⟹ hi/4 = 2
:\implies:⟹ hi = 8cm
Hence, the height of image is 8 cm
Nature of Image :- Real , inverted & larger than the object .