An object is placed 37.5 cm in front of a concave mirror with a radius of curvature of 75 cm. Describe the characteristics of the image in using GRESA form
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To describe the characteristics of the image using the GRESA form (which stands for: position, size, orientation, type, and nature), we need to determine the image distance, size, and type.
1. Position:
To find the position of the image, we need to use the mirror formula:
1/f = 1/d₀ + 1/dₑ
Where:
- f is the focal length of the mirror
- d₀ is the object distance from the mirror
- dₑ is the image distance from the mirror
Given:
- f = radius of curvature / 2 = 75 cm / 2 = 37.5 cm
- d₀ = -37.5 cm (negative since the object is placed in front of the mirror)
Plugging in the values, we can solve for dₑ:
1/37.5 = 1/-37.5 + 1/dₑ
1/dₑ = 1/37.5 + 1/37.5
1/dₑ = 2/37.5
dₑ = 37.5/2
dₑ = 18.75 cm
The image position is 18.75 cm in front of the mirror.
2. Size:
To find the size of the image, we use the magnification formula:
magnification = -dₑ/d₀
Plugging in the values, we can solve for the magnification:
magnification = -18.75 cm / -37.5 cm
magnification = 1/2
The magnification is 1/2, which means the image is half the size of the object.
3. Orientation:
Since the magnification is positive (1/2), it indicates that the image is upright compared to the object.
4. Type:
A concave mirror can produce both real and virtual images, depending on the object position. In this case, since the image is formed in front of the mirror, it is a real image.
5. Nature:
As the image is real and upright, it is also diminished in size since the magnification is less than 1.
To summarize, the characteristics of the image formed by the concave mirror are:
- Position: 18.75 cm in front of the mirror
- Size: half the size of the object
- Orientation: upright
- Type: real
- Nature: diminished