An object of height 2•5cm is placed at 20cm from a convex mirror of focal length 10cm. Calculate the height of the image formed.
To calculate the height of the image formed by the convex mirror, we can use the mirror equation:
1/f = 1/v + 1/u
Where:
- f is the focal length of the mirror,
- v is the distance of the image from the mirror (which is what we want to find),
- u is the distance of the object from the mirror.
Using the given values:
f = 10cm
u = 20cm
Plugging these values into the equation:
1/10 = 1/v + 1/20
To simplify the equation, we can find the common denominator:
1/10 = (2 + 1)/v
Multiplying both sides by 10v to eliminate the fractions:
v = 3v + 15
Subtracting 3v from both sides:
-2v = 15
Dividing both sides by -2:
v = -15/2
Since the image is formed on the opposite side of the mirror, the distance is negative. However, in this case, we are only interested in the magnitude of the distance, so we take the absolute value:
|v| = |-15/2| = 15/2
So, the distance of the image from the mirror is 15/2 cm.
To calculate the height of the image, we can use the magnification formula:
magnification = -v/u
Plugging in the values:
magnification = -(15/2) / 20 = -15/40 = -3/8
The negative sign indicates that the image is inverted.
Now, we can calculate the height of the image. The magnification formula states that the height of the image is equal to the magnification multiplied by the height of the object.
Using the given value:
height of object = 2.5cm
Height of image = (-3/8) * 2.5 = -7.5/8 = -15/16
Again, the negative sign indicates that the image is inverted.
Therefore, the height of the image formed by the convex mirror is -15/16 cm.
To calculate the height of the image formed by a convex mirror, we can use the mirror equation which relates the object distance (u), the image distance (v), and the focal length (f) of the mirror.
The mirror equation is given by:
1/f = 1/v - 1/u
Given:
Height of the object (h) = 2.5 cm
Object distance (u) = 20 cm
Focal length (f) = 10 cm
First, we need to find the image distance (v) using the mirror equation.
Substituting the given values into the mirror equation, we have:
1/10 = 1/v - 1/20
Simplifying the above equation:
1/v = 1/10 + 1/20
1/v = 3/20
Now, we can find the value of v by taking the reciprocal of both sides:
v = 20/3 cm
Next, we can use the magnification formula to find the height of the image (h') in terms of the object height (h), object distance (u), and image distance (v).
The magnification formula is given by:
m = -v/u = h'/h
Substituting the given values into the magnification formula, we have:
m = -(20/3) / 20 = -1/3
Since the magnification (m) is negative, it indicates that the image is inverted.
Finally, we can find the height of the image (h') by rearranging the magnification formula:
h' = m * h
Substituting the given values into the formula, we get:
h' = (-1/3) * 2.5
Calculating the value:
h' = -0.83 cm
Therefore, the height of the image formed by the convex mirror is approximately -0.83 cm.
To calculate the height of the image formed by a convex mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the convex mirror
- v is the image distance
- u is the object distance
Given in the question:
- The focal length (f) of the convex mirror is 10 cm
- The object distance (u) is 20 cm
To find the image distance (v), we can use the magnification formula:
magnification (m) = -v/u
Where:
- m is the magnification
To solve for v, we rearrange the equation to find:
v = -u/m
To calculate the magnification, we can use the height formula:
magnification (m) = -height of the image/height of the object
Given in the question:
- The height of the object is 2.5 cm
To find the height of the image, we rearrange the equation to solve for the height of the image:
height of the image = -magnification x height of the object
Now, let's calculate step by step:
Step 1: Calculate the magnification (m):
height of the object = 2.5 cm
m = -height of the image / height of the object
Step 2: Calculate the image distance (v):
v = -u / m
Step 3: Calculate the height of the image:
height of the image = -magnification x height of the object
Let's substitute the given values into the equations:
Step 1: Calculate the magnification (m):
height of the object = 2.5 cm
m = -height of the image / height of the object
m = -h / 2.5
Step 2: Calculate the image distance (v):
v = -u / m
v = -20 / (-h/2.5)
v = 50h
Step 3: Calculate the height of the image:
height of the image = -magnification x height of the object
height of the image = -(-h/2.5) x 2.5
height of the image = h
Since v = 50h and height of the image = h,
We can equate them to find h:
h = 50h
1 = 50
This is an invalid result. It seems we made a mistake in our calculations. Let me recalculate.
Upon recalculating using the formula h = h/2.5 x 2.5, we can see that the height of the image formed is the same as the height of the object, which is 2.5 cm. Therefore, the height of the image formed is 2.5 cm.