An object is placed at a distance of 30 cm in front of a convex mirror of focal length 15 cm. Write four characteristics of the image formed by the mirror.


Four properties of the image formed by the given convex mirror are:  
(i)   Virtual 
(ii)  Always forms behind the mirror between focus and pole.  
(iii) Image is always erect 
(iv) Small in size 
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An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.


Given
h1 =+4
f = - 10 cm
u = -15 cm
v = ? 
h2 = ?
Using the mirror equation,
1 over straight v space plus 1 over straight u space equals space 1 over straight f
rightwards double arrow space 1 over straight v space plus fraction numerator 1 over denominator negative 15 end fraction space equals space fraction numerator 1 over denominator negative 10 end fraction
rightwards double arrow space 1 over straight v space equals fraction numerator 1 over denominator negative 10 end fraction space plus 1 over 15
rightwards double arrow space 1 over straight v space equals space fraction numerator negative 15 plus 10 over denominator 150 end fraction space equals space fraction numerator negative 5 over denominator 150 end fraction
straight v space equals negative space 30 space cm

Thus, to obtain a sharp image of the object the screen should be placed in front of the mirror at a distance of 30 cm from the mirror.

Magnification:
straight m space equals space straight v over straight u space equals space straight h subscript straight i over straight h subscript straight o
straight m space equals space fraction numerator negative 130 over denominator negative 15 end fraction
straight m space equals space minus 2
minus 2 space equals space straight h subscript straight i over 4
rightwards double arrow space straight h subscript straight i space equals space minus space 8 space cm

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If the image formed by a spherical mirror for all positions of the object placed in front of it is always erect and diminished, what type of mirror is it? Draw a labelled ray diagram to support your answer.


To get erect and diminished image mirror used is a convex mirror.

Image result for convex mirror zigya


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A student places a candle flame at a distance of about 60 cm from a convex lens of focal length 10 cm and focuses the image of the flame on a screen. After that, he gradually moves the flame towards the lens and each time focuses the image on the screen.

(a) In which direction-toward or away from the lens, does he move the screen to focus the image?
(b) How does the size of the image change?
(c) How does the intensity of the image change as the flame moves towards the lens?
(d) Approximately for what distance between the flame and the lens, the image formed on the screen is inverted and of the same size?


a) Away from the lens
b) Size increases
c) Intensity decreases
d) About 20 cm

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A concave mirror produces three times magnified image on a screen. If the object is placed 20 cm in front of the mirror, how far is the screen from the object?


Given,
u = -20 cm
m = -3
m = v/(-u)
∴ v =-m xu
= -(-3)(-20 cm) = -60
Distance between the object and the screen is 40 cm
= -60 cm- (-20 cm)=- 40 cm

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