Answer :
Final answer:
The focal length of the concave mirror is approximately -25.1 cm.
Explanation:
To find the focal length of a concave mirror, we can use the mirror equation:
[tex]\(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\)[/tex]
Where:
- [tex]\(f\)[/tex] is the focal length of the mirror (which we want to find).
- [tex]\(d_o\)[/tex] is the object distance (given as 39.3 cm).
- [tex]\(d_i\)[/tex] is the image distance (given as -17.8 cm, with a negative sign because the image is in front of the mirror).
Now, plug in the values:
[tex]\(\frac{1}{f} = \frac{1}{39.3 \, \text{cm}} + \frac{1}{-17.8 \, \text{cm}}\)[/tex]
Now, calculate the right side of the equation:
[tex]\(\frac{1}{f} = 0.0254 \, \text{cm}^{-1} - 0.0562 \, \text{cm}^{-1} = -0.0308 \, \text{cm}^{-1}\)[/tex]
Now, find the focal length [tex](\(f\))[/tex] by taking the reciprocal:
[tex]\(f = \frac{1}{-0.0308 \, \text{cm}^{-1}} \approx -25.1 \, \text{cm}\)[/tex]
So, the focal length of the concave mirror is approximately -25.1 cm. The negative sign indicates that it is a concave mirror, and the focal point is in front of the mirror.
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Final answer:
The focal length of the concave mirror in this scenario can be found by applying the values of the object distance and image distance to the mirror formula.
Explanation:
The focal length of a
concave mirror
can be calculated using the mirror formula:
1/f = 1/u + 1/v
, where 'f' is the focal length, 'u' is the object distance, and 'v' is the image distance. For a concave mirror, the object distance 'u' is always taken as negative and if the image is formed on the same side as the object, then 'v' is also taken as negative. In this question, we have 'u' = -39.3 cm and 'v' = -17.8 cm. By substituting these values into the mirror formula, we get the focal length 'f'. You can find the focal length by doing the arithmetic and solving for 'f'.
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