Whereb must an object be placed from a concave mirror of radius of curvature of 6cm. to give an image on a screen four times as large as the object
A man 1.5 meter tall stands in front of a concave mirror whose radius is 30cm. Find the osition of the man that will lead his image on the screen 20 cm from the mirror. How big is the man's image
This was answered in your later repeat post.
To determine the position where an object should be placed in front of a concave mirror to create an image that is four times larger than the object, we can use the mirror formula and magnification formula. Here's how:
1. Mirror formula:
The mirror formula relates the object distance (u), image distance (v), and the focal length (f) of the mirror. The formula is given as:
1/f = 1/v + 1/u
2. Magnification formula:
The magnification formula relates the height of the image (hᵢ) and the height of the object (h₀). The formula is given as:
magnification (m) = hᵢ / h₀ = -v / u
In this case, we want the image to be four times the size of the object, so the magnification (m) will be 4.
To solve the problem, we'll use the following steps:
Step 1: Identify the given parameters:
- Radius of curvature (R) = 6 cm
- Magnification (m) = 4
Step 2: Find the focal length (f):
The focal length of a concave mirror is half the radius of curvature:
f = R / 2 = 6 cm / 2 = 3 cm
Step 3: Find the object distance (u):
Using the magnification formula, we can rearrange it to solve for u:
m = -v / u
4 = -v / u
Since the magnification is positive for a magnified image,
we can write |m| = v / u
|4| = v / u
4 = v / u
Step 4: Substitute the values into the mirror formula:
1/f = 1/v + 1/u
1/3 = 1/v + 1/u
Substitute v/u = 4:
1/3 = 1/4u + 1/u
To simplify, let's express everything with a common denominator:
1/3 = (1 + 4) / 4u
1/3 = 5/4u
Cross-multiplying:
4u = 3 * 5
4u = 15
Dividing both sides by 4:
u = 15 / 4
u = 3.75 cm
Therefore, the object must be placed at a distance of 3.75 cm from the concave mirror to create an image four times larger on a screen.