At what distance should an object be placed from the pole of a converging mirror of focal length 16 cm to form a real image that is half the size of the object?

Problems on spherical mirrors:
problem: An extended object is placed perpendicular to the principal axis of a concave mirror of radius of curvature 20cm at a distance of 15cm from the pole. Find the lateral magnification produced.
Solution:

problem: A Point object is placed 60cm from the pole of concave mirror of focal length 10cm on the principle axis find (a) Position of image (b) If the object is shifted1 mm towards the mirror along principle axis, find the shift in image.

Solution:(a) u = – 60cm

problem: A thin rod of length f/3 is placed along the optical axis of a concave mirror of focal length f such that its image which is real and elongated just touches the rod. Calculate the magnification.
Solution: As in question, image touches the rod, i.e., image and object coincides, hence one end of the rod should be at the center of curvature. It is also written that image is enlarged, it indicates that the orientation of rod should be toward focus then only we can get enlarged image along the principal axis. Let l be the length of the image.

problem: A concave and convex mirror are placed on two parallel optics axis as shown. Find the coordinates of images of point object P formed after two successive reflection; first reflections at concave mirror and then at convex mirror.

ho2 = 6 + 2 = 8mm.

problem: A point object is located at a distance of 15cm from the pole of a concave mirror of focal length 10cm on its principle axis is moving with a velocity

(Vim)∥ = –m2(Vom)∥ = – (– 2)24 = – 16 cm/sec.

(Vim)⊥ = m (Vom)⊥ + ho(dm/dt) = (– 2)9 = – 18 cm/s. [ho = 0]

How far should an object be placed from the pole of a converging mirror of focal length 20cm to form a real image of the size exactly `1/4`th the size of the object?

Given,Focal length of the concave mirror (f) = 20 cmMagnification (m) = -1/4

Using the magnification formula, we get  

`m=-v/u` 

`-1/4=(-v)/u` 

`v=u/4`  

Using the mirror formula, we get 

`1/f=1/v+1/u` 

`1/-20=4/u+1/u` 

`-1/20=5/u` 

u=−100 cmThus, the object should be placed in front of the concave mirror at a distance of 100 cm. 

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