An object 4.0cm in height is placed at a 25cm from a concave mirror of focal length 15cm.find the position, nature, and size of image formed.
To find the position, nature, and size of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
Given information:
Height of the object (h) = 4.0 cm
Distance of the object from the mirror (u) = -25 cm (since the object is placed at a distance of 25 cm in front of the mirror)
Focal length of the mirror (f) = -15 cm (concave mirror has a negative focal length)
Step 1: Calculate the magnification (m).
The magnification is given by the formula:
m = -v/u
Step 2: Use the magnification to calculate the height of the image (h') using the formula:
h' = m * h
Step 3: Use the mirror formula to calculate the image distance (v).
1/f = 1/v - 1/u
Step 4: Determine the nature of the image.
- If v is positive, the image is real and formed on the same side as the object.
- If v is negative, the image is virtual and formed on the opposite side of the object.
Now, let's calculate the values:
Step 1: Calculate the magnification (m).
m = -v/u = -v/(-25 cm) = v/25
Step 2: Calculate the height of the image (h').
h' = m * h = (v/25) * 4.0 cm
Step 3: Solve the mirror formula equation.
1/f = 1/v - 1/u
1/-15 cm = 1/v - 1/(-25 cm)
-1/15 cm = 1/v + 1/25 cm
Multiply through by 375v to simplify the equation:
-25v = 375 - 15v
-10v = 375
v = -37.5 cm
Step 4: Determine the nature of the image.
Since v is negative (-37.5 cm), the image is virtual and formed on the opposite side of the object.
The position of the image is -37.5 cm from the mirror.
The nature of the image is virtual.
The size of the image can be determined by substituting the value of v into the equation for h':
h' = (v/25) * 4.0 cm
Let's calculate the size of the image:
h' = (-37.5 cm / 25) * 4.0 cm = -6.0 cm
Therefore, the size of the image is -6.0 cm in height.