We can solve this step-by-step using the mirror equation and magnification formula.

Given:

• Object distance ($d_o$) = 14.1 cm
• Focal length ($f$) = 10.1 cm (since the mirror is concave, the focal length is positive)

(a) Calculate the image distance ($d_i$) using the mirror equation:

The mirror equation is: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$

Rearranging the equation to solve for the image distance $d_i$: $\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}$

Substitute the given values: $\frac{1}{d_i} = \frac{1}{10.1} - \frac{1}{14.1}$

Now, calculate $d_i$.

$\frac{1}{d_i} = 0.09901 - 0.07092 = 0.02809$ $d_i = \frac{1}{0.02809} \approx 35.6 \text{ cm}$

Thus, the image distance is approximately $d_i = 35.6$ cm. Since it's positive, this means the image is formed on the same side as the reflected rays, indicating it's a real image.

(b) Calculate the magnification ($M$) using the magnification formula:

The magnification formula is: $M = -\frac{d_i}{d_o}$

Substitute the values for $d_i$ and $d_o$: $M = -\frac{35.6}{14.1} \approx -2.52$

Thus, the magnification is approximately $M = -2.52$. The negative sign indicates that the image is inverted.

(c) How would you describe the image?

• Type: Real (since the image distance is positive).
• Orientation: Inverted (due to the negative magnification).
• Size: The image is magnified by a factor of approximately 2.52 times its actual size (since $|M| > 1$).

Summary of Answers:

(a) Image distance = +35.6 cm

(b) Magnification = -2.52

(c) The image is real, inverted, and magnified by a factor of 2.52.

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Would you like further explanation or details on any of these steps? Feel free to ask!

Related Questions:

1. How would the image change if the object were placed closer to the focal point?
2. How would the magnification change if the object were farther from the mirror?
3. What happens to the image if the mirror were convex instead of concave?
4. How do you calculate the focal length if the image and object distances are known?
5. How does the sign convention work for convex mirrors versus concave mirrors?

Tip: When dealing with mirrors, always remember that the sign convention for object distance (positive for real objects) and image distance (positive for real images) is crucial in determining the image's nature.