An Insect is magnified 12 times by a concave mirror. If the image is real, inverted and 6 cm away from the mirror, how far away is the insect? I need help in steps, when I tried the question I got a wrong answer
Answer:
Step 1: Calculate the magnification of the image:
Magnification = Image distance/Object distance
Magnification = 6 cm/x cm
12 = 6 cm/x cm
x cm = 6 cm/12
x cm = 0.5 cm
Step 2: Calculate the distance of the insect from the mirror:
Object distance = Image distance/Magnification
Object distance = 6 cm/12
Object distance = 0.5 cm
To solve this problem, we can use the mirror equation:
1/f = 1/di + 1/do
Where:
f = focal length of the mirror
di = image distance
do = object distance
Given that the insect is magnified by 12 times, we can calculate the magnification using the formula:
magnification = -di/do
Since the image is real and inverted, the magnification will be negative.
Let's solve step by step:
Step 1: Write down the given information:
Magnification (m) = -12
Image distance (di) = -6 cm
Step 2: Find the magnification factor:
m = -di/do
-12 = -(-6)/do
-12 = 6/do
Step 3: Solve for the object distance (do):
multiply both sides of the equation by do:
-12 * do = 6
do = 6/(-12)
do = -0.5 cm
Step 4: Substitute the values into the mirror equation to find the focal length (f):
1/f = 1/di + 1/do
1/f = 1/-6 + 1/-0.5
Step 5: Add the fractions on the right side:
1/f = -1/6 - 2/2
1/f = -1/6 - 6/6
1/f = -7/6
Step 6: Flip both sides of the equation:
f = -6/7
Step 7: Calculate the object distance (do):
do = -0.5 cm
Step 8: Calculate the distance of the insect, which is the object distance plus the focal length:
Distance of insect = do + f = -0.5 + (-6/7)
Distance of insect = (-3/2 - 6/7)
Distance of insect = (-21/14 - 12/7)
Distance of insect = (-33/14)
So, the distance of the insect from the concave mirror is -33/14 cm.
To solve this question, you can use the mirror formula for concave mirrors:
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 (positive for real images),
- u is the distance of the object from the mirror (positive for objects in front of the mirror).
Let's break down the given information:
Image magnification, M = -v/u = -12
Image distance, v = -6 cm (since it's real and inverted)
We need to find the object distance, u.
Step 1: Find the focal length of the mirror (f).
Since the image is real and inverted, and the magnification (M) is negative, we have:
M = -v/u = -12
-12 = -6/u
Cross-multiplying:
-12u = -6
Dividing both sides by -12:
u = 6/12
u = 0.5 cm
Step 2: Plug the values into the mirror formula and solve for f.
1/f = 1/v - 1/u
1/f = 1/-6 - 1/0.5
1/f = -1/6 - 2/6
1/f = -3/6
Cross-multiplying:
-3f = 6
Dividing both sides by -3:
f = -2 cm
Step 3: Use the magnification formula to find the distance of the object.
M = -v/u
-12 = -6/0.5
Cross-multiplying:
-12 * 0.5 = -6
-6 = -6
Therefore, the object distance is 0.5 cm. The insect is located 0.5 cm away from the concave mirror.