Did you know?
Did you know that concave mirrors have the unique ability to create real, inverted images? Using GRASP (Geometry, Reasoning, Algebra, Sketch, Practice), we can solve a problem related to this phenomenon!
In our scenario, a concave mirror is creating a real, inverted image of a dog located 2 meters away from its surface. But what if the image of the dog needs to be 10 times larger? How far is the dog from the mirror then?
To solve this problem, let's use the GRASP method:
Geometry:
- The dog is located 2 meters away from the mirror.
- The mirror is concave, meaning it curves inward.
Reasoning:
- A concave mirror creates a real, inverted image.
- If we want the image to be larger, the dog needs to be closer to the mirror.
Algebra:
- Let's assume that the new distance between the dog and the mirror is 'd' meters.
- We know that the magnification factor is 10, meaning the new image is 10 times larger than the previous one.
- According to the mirror equation, 1/focal length = 1/object distance + 1/image distance.
- The focal length of a concave mirror is always positive.
Sketch:
Imagine a concave mirror with a dog located 2 meters away from it, and a larger, inverted image of the dog.
Practice:
Now, let's solve the problem using equations. As the image formed is real and inverted, the image distance (di) needs to be negative according to the sign convention.
According to the mirror equation:
1/f = 1/do + 1/di
Since do = 2m, and di is negative (since the image is real and inverted):
1/f = 1/2 + (-1/di)
Since the magnification factor (M) is given as 10, we know that:
M = -di/do
Substituting the values, we get:
10 = -di/2
Simplifying, we find:
-di = 20
Therefore, di = -20m.
Since the image distance represents the distance between the mirror and the new image, the dog must be sitting 20 meters away from the mirror.
Using the GRASP method, we calculated that if the image of the dog needs to be 10 times larger, the dog must sit 20 meters away from the concave mirror.
