A1 cm long flame is placed at a distance of 1.5 m from a wall. how far from the wall should a concave mirror be placed in order to obtain a 2 cm long flame on the same wall? what is the focal length of the mirror?
Answers
hey mate here
is your answer
.
.
You want a real image, so it will be a projection. Meaning that the image will be inversed, height -2cm. So the magnification will be -2.
In order to get a magnification of -2, the object has to stand 1+1/2 = 1.5 focal lengths left of the mirror (same with a thin lens). The image will be 1+2 = 3 focal lengths left of the mirror. So the image will be 3–1.5 = 1.5 focal lengths left of the object. Then the focal length must be f=1m. Then the mirror is 3m right to the image/wall, 1.5m right to the object.
(object and image height taken 10 times bigger than they are in the question for better visibility)
Now in formulas.
General magnification formulas for single refracting or reflecting surfaces aswell as thin lenses:
M=1−pnR(img−surf)
1M=1+pnL(obj−surf)
With left and right refraction indices nL and nR. For mirrors we use nL=1, nR=-1, for thin lenses nL=nR=1.
Then we have with M=-2, img-obj = -1.5m
1M−1=p(obj−surf)=−1.5
M−1=p(img−surf)=−3
Now we construct the image-object distance and use what we have
p(img−obj)=p(img−surf)−p(obj−surf)
p(−1.5m)=−3−(−1.5)=−1.5
Rest is easy
→f=1p=1m
→img−surf=M−1p=−3m
→obj−surf=1/M−1p=−1.5m
339 Views ·
How far should the object be placed from a concave mirror of focal length 4.8 cm when the image is to be obtained at a distance 12 cm from the mirror?
What is the image distance if an object is placed 33.7 cm from the convex mirror with a focal length of 10.7 cm?
A 2.5 cm tall object is placed at a distance of 47.5 cm from a concave mirror having the focal length of 5 cm. What is the image distance and image size?
An object 2 cm in size is placed 20 cm in front of a concave mirror of focal length 10 cm. What is the distance from the mirror at which a screen should be placed in order to obtain a sharp image? What will be the nature of the image formed?
The focal length of a concave mirror is 20 cm and the object is at a distance of 10 cm. What is the distance?
Mr. Nikolas Scholz’ answer, though expansive, is quite good for educational purposes. Please refer to it to have a good, clear, understanding of ray optics, mirror formula and image formation.
Mr. Roland Neville’s answer is complete if you only desire a solution and please refer to it if getting the solution is your sole aim.
205 Views
Let the mirror be L from the wall.
The image distance is obviously L and the object distance is (L - 150)
Magnification = L/(L-150) = 2
L = 300cm
Looking back at it, by similar triangles it is clear the object is halfway between wall and mirror.
Use the Formula to get f
Everything is Real, therefore Positive.
1/f = 1/150 + 1/300 = 3/300
f = 100cm or 1 metre
hope it helps you dear