A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.
Drawing the ray diagram: Using a scale of 1: 5, we get v = - 2 cm, f = - 3 cm. We draw the ray diagram as follows:
(i) Draw the principal axis (a horizontal line).
(ii) Draw a convex lens, keeping principal centre (C) on the principal axis.
(iii) Mark points F and B on the left side of lens at a distance of 3 cm and 2 cm respectively.
(iv) Join any point D (nearly at the top of lens) and F by a dotted line.
(v) Draw a line AD, parallel to principal axis.
(vi) Draw a line A'B', perpendicular to principal axis from B'.
(vii) Draw a line CA', backwards, so that it meets the line from D parallel to principal axis at A.
(viii) Draw a line AB, perpendicular (downwards) from A to meet the principal axis at B.
(ix) The AB is position of object. Measure distance BC. It will be found to be equal to 6 cm.
Thus, object is placed at a distance of 6 cm × 5 = 30 cm from the lens.
The magnification produced by a plane mirror is +1. What does this mean?
Magnification is the ratio of the size of the image (h') to the size of the object(h).
As,
Magnification,
For a plane mirror, m = + 1 (given).
So,
h' = h and v = -u
Magnification is equal to one indicates that the size of image is same as that of object.
Positive sign of m indicates that a virtual image is formed behind the mirror.
We are given a convex mirror.
Here, we have
Object size, h = + 5 cm
Object distance, u = -20 cm
Radius of curvature, R = + 3.0 cm [R is +ve for a convex mirror]
Focal length ,
From mirror formula,
we have,
Image distance,
Magnification,
Therefore,
A virtual and erect image of height 2.2 cm is formed behind the mirror (because v is positive) at a distance of 8.6 cm from the mirror.
Given,
Power of the lens, P = -2.0 D
Therefore,
Focal length,
Since, focal length is negative, the lens is concave.
We are given a convex mirror.
Here,
Object distance, u = -10 cm
Focal length, f = + 15 cm [f is +ve for a convex mirror]
Image distance, v = ?
Using the mirror formula,
we have,
Thus, image distance, v = + 6 cm.
As image distance is +ve, so a virtual, erect image is formed at a distance 6 cm behind the mirror.