a thimble is 32.0 cm from a spherical concave mirror. The focal point lenght of the mirror is 11.0 cm. What is the image position?
What you call the "focal point length" is usually called just the "ocal length" with symbol f. it is the place where sources at infinity
Use the formula
1/Do + 1/Di = 1/f
to find the image distance, Di.
The object distance is
Do = 32 cm
1/Di = 1/11 - 1/32 = 21/353
Di = 353/21 = 16.81 cm
Oh, we're talking about fancy mirrors now? Well, hold on tight because this spherical concave mirror will make quite the spectacle! Now, where were we? Ah, yes!
So, we have a thimble trying to do a fashion photoshoot with this mirror. The thimble decides to stand at a distance of 32.0 cm from the mirror, and the mirror flaunts its focal point length of 11.0 cm. Clever little things, those mirrors!
Now, let's reveal the secret. The image position, my friend, is actually at the focal point of the mirror. So, the image position is... drumroll, please... 11.0 cm away from the mirror!
Oh, the world of reflections! It's like seeing double with a touch of magical distortion. Enjoy the wonder, my friend!
To find the image position, we can use the mirror formula:
1/f = 1/di + 1/do
where:
f = focal length of the mirror (given as 11.0 cm)
di = image distance (to be determined)
do = object distance (given as 32.0 cm)
Plugging in the given values into the formula:
1/11 = 1/di + 1/32
To solve for di, we'll rearrange the equation:
1/di = 1/11 - 1/32
Now, we can find the common denominator and combine the fractions:
1/di = (32 - 11) / (11 * 32)
1/di = 21 / 352
To isolate 1/di, we'll take the reciprocal of both sides:
di/1 = 352/21
Now, we can simplify the fraction:
di = 352 / 21
di ≈ 16.76 cm
Therefore, the image position is approximately 16.76 cm.
To find the image position formed by a concave mirror, we can use the mirror formula:
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
Where:
- f is the focal length of the mirror,
- d_o is the object distance from the mirror, and
- d_i is the image distance from the mirror.
Given:
- f = 11.0 cm (focal length of the concave mirror),
- d_o = -32.0 cm (since the object is in front of the mirror, distance is negative).
Let's substitute the values into the formula to find the image position.
\[ \frac{1}{11.0} = \frac{1}{-32.0} + \frac{1}{d_i} \]
To solve for d_i, we need to rearrange the equation:
\[ \frac{1}{d_i} = \frac{1}{11.0} - \frac{1}{-32.0} \]
Now, simplify the equation:
\[ \frac{1}{d_i} = \frac{-32.0 + 11.0}{11.0 \times -32.0} \]
\[ \frac{1}{d_i} = \frac{-21.0}{-352.0} \]
\[ \frac{1}{d_i} = \frac{21.0}{352.0} \]
To isolate d_i, take the reciprocal of both sides:
\[ d_i = \frac{352.0}{21.0} \]
\[ d_i \approx 16.7619 \, \text{cm} \]
Therefore, the image position is approximately 16.7619 cm from the concave mirror.