Respuesta :
Answer:
The radius of curvature is 6.4 cm
Explanation:
Given that,
Object distance = 2.40 cm
Magnification = 4
We need to calculate the image distance
Using formula of magnification
[tex]m = -\dfrac{v}{u}[/tex]
Put the value into the formula
[tex]4=-\dfrac{v}{2.40}[/tex]
[tex]v=4\times2.40[/tex]
[tex]v = -9.6\ cm[/tex]
Negative sign shows the image of the object is same side of object
(b). We need to calculate the radius of curvature
Using mirror formula
[tex]\dfrac{2}{R}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]
Put the value into the formula
[tex]\dfrac{2}{R}=\dfrac{1}{2.40}-\dfrac{1}{9.6}[/tex]
[tex]R=\dfrac{2}{0.3125}[/tex]
[tex]R=6.4\ cm[/tex]
Hence, The radius of curvature is 6.4 cm.
The radius of the mirror is 6.4cm.
How to get the radius?
The information is:
- Distance between the mirror and the object = d = 2.40cm
- Magnification = m = 4.
The magnification formula is given by:
[tex]m = -\frac{v}{d}[/tex]
(The negative sign is because the image is upright).
Replacing the known values, we get:
[tex]4 = -\frac{v}{2.40cm} \\v = -4*2.40cm = -9.60cm[/tex]
Now, the radius is given by:
[tex]2/R = \frac{1}{d} + \frac{1}{v}[/tex]
Replacing the values of d and v we get:
[tex]\frac{2}{R} = \frac{1}{2.40cm} + \frac{1}{-9.60cm} = 0.3125 cm^{-1}\\\\R = 2/( 0.3125 cm^{-1}) = 6.4cm[/tex]
So the radius is 6,4cm
If you want to learn more about mirrors, you can read:
https://brainly.com/question/357022
