A thimble is 32.0 cm from a spherical concave mirror. The focal length of the mirror is 11.0 cm. What is the image
position?
1 point
If the thimble in the previous question is 2.50 cm tall, how tall is the image of the thimble? What is its orientation? Draw a diagram.
To find the image position, we can use the mirror equation:
1/f = 1/d_i + 1/d_o
Where:
f = focal length of the mirror
d_i = image distance
d_o = object distance
Given:
f = 11.0 cm
d_o = 32.0 cm
Let's substitute the values into the equation:
1/11.0 = 1/d_i + 1/32.0
To solve for d_i, we can rearrange the equation:
1/d_i = 1/11.0 - 1/32.0
Now we can find the common denominator:
1/d_i = (32 - 11) / (11 * 32)
Simplifying the expression:
1/d_i = 21 / 352
To find the value of d_i, we take the reciprocal of both sides:
d_i = 352 / 21
Calculating the value:
d_i ≈ 16.76 cm
Therefore, the image position is approximately 16.76 cm.
To find the height of the image, we can use the magnification equation:
magnification = -d_i / d_o
Given:
d_i = 16.76 cm
d_o = 32.0 cm
Let's substitute the values into the equation:
magnification = -16.76 / 32.0
Calculating the value:
magnification ≈ -0.524
Since the magnification is negative, it implies that the image is inverted.
To find the height of the image, we can use the formula:
height of image / height of object = magnification
Given:
Height of object = 2.50 cm
Let's substitute the values into the equation:
height of image / 2.50 = -0.524
Now we can solve for the height of the image:
height of image = -0.524 * 2.50
Calculating the value:
height of image ≈ -1.31 cm
The height of the image is approximately -1.31 cm, which means the image is inverted and smaller than the object.
To draw a diagram, you can sketch a concave mirror with its focal length labeled. Place the object (thimble) along the principal axis at a distance of 32.0 cm from the mirror. Draw the reflected rays according to the rules of reflection for a concave mirror. The image will be formed on the same side as the object, between the focal point and the mirror. The height of the image will be smaller than the height of the object, and it will be inverted.