a concave shaving mirror is construction so that a man at a distance of 20cm from the mirror sees his image magnified 1.5 times what is the radius of curvature of the mirror?
I connot do it....plz help me....
To find the radius of curvature of the concave shaving mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Here,
f = focal length of the mirror,
v = image distance from the mirror,
u = object distance from the mirror.
Given:
The man is at a distance of 20 cm from the mirror (object distance, u = -20 cm) and sees his image magnified 1.5 times. This implies that the magnification (m) is also 1.5.
Remember:
If the magnification (m) is positive, it means the image is upright.
If the magnification (m) is greater than 1, it means the image is magnified.
If the magnification (m) is less than 1 but greater than 0, it means the image is reduced in size.
Since the image is magnified (m = 1.5), it means the image is virtual and formed on the same side as the object.
Now, let's substitute the given values into the mirror formula:
1/f = 1/v - 1/u
1/f = 1/v - 1/-20 (substituting u = -20 cm)
1/f = 1/v + 1/20 (converting -1/-20 to 1/20)
Since the image is formed on the same side as the object (virtual image), the image distance (v) will be positive.
Now, we know that the magnification (m) is given by:
m = -v/u
1.5 = -v/-20 (substituting m = 1.5 and u = -20 cm)
1.5 = v/20
v = 1.5 * 20 = 30 cm
Now, substituting the value of v into the mirror formula:
1/f = 1/30 + 1/20
1/f = (2 + 3)/60
1/f = 5/60
1/f = 1/12 (taking the reciprocal)
So, the focal length (f) of the mirror is 12 cm.
Now, the radius of curvature (R) is related to the focal length (f) by the formula:
R = 2f
R = 2 * 12 cm = 24 cm
Therefore, the radius of curvature of the mirror is 24 cm.