A convex lens has a focal length of 12cm . at what distance from the lens should an object be placed so that on the other side of the lens it's real and inverted image is formed 24 cm away from the lens? What would be the size of the image formed? Draw a ray diagram to show the image formed in this case. Please solve in a Notebook and please send a photo.
Answers
Answer:
From the given information we have the data as follows.
The focal length of the convex lens is, f=+10cmf=+10cm
The image distance is, v=+20cmv=+20cm
The height of the object, O=2cmO=2cm
As the image distance is positive, thus, the image formed will be real and inverted.
Consider the formula that relates the focal length of the lens, image distance and object distance.
1f=1v−1u1f=1v−1u
Where f is the focal length, v is the image distance and u is the object distance.
Substitute the values in the above equation.
110=120−1u⇒1u=120−110∴1u=120110=120−1u⇒1u=120−110∴1u=120
Therefore, the object distance is 20 cm.
The value of the object distance is twice that of the focal length of the convex lens. So, the object is placed at 2F and the image also forms at 2F on the other side of the lens, as the image distance equals the object distance. Thus, the height of the image will be 2 cm.
The formation of the image by drawing a ray diagram is given as follows.
∴∴ The distance from the lens at which the object is placed so that forms a real and inverted image 20 cm away from the lens is 20 cm. The size of the image formed if the object is 2 cm high is the same as that of the size of the object.