
Lens formula is given by _ _ _ _ _ _ _ _
Answer
499.5k+ views
Hint: In this question, we need to establish the Lens formula. For this we will use the relation between image distance, object distance, and focal length in case of either convex or concave lens.
Complete step by step answer:
Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length (f) of the convex lens. The image A1B1 is formed between O and F1 on the same side as the object is kept, and the image is erect and virtual.
By sign conventions, all distances are given by
OF1 focal length
OA object distance
OA1
Now, are similar [because vertex O is common for both the triangles so So, are similar]
From similarity criteria, we have
Similarly, and are also similar
So,
But from the ray diagram, we see
So, equation (ii) becomes
From equation (i) and equation (iii), we get
By sign conventions,
So, we have
Dividing both sides by uvf
Hence, the required formula for the lens is given as .
Note:Before finding the lens formula, we must remember the sign convention for the lens, which is
(i) All distances are to be measured from the optical center of the lens.
(ii) Distances measured in the direction of incident ray (which is from left to right) are taken as positive.
(iii) Distances measured in the direction opposite to incident ray are taken as negative.
(vi) Height measured upward; the principal axis is taken as positive.
(v) Height measured downward; the principal axis is taken as negative.
Complete step by step answer:
Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length (f) of the convex lens. The image A1B1 is formed between O and F1 on the same side as the object is kept, and the image is erect and virtual.

By sign conventions, all distances are given by
OF1
OA
OA1
Now,
From similarity criteria, we have
Similarly,
So,
But from the ray diagram, we see
So, equation (ii) becomes
From equation (i) and equation (iii), we get
By sign conventions,
So, we have
Dividing both sides by uvf
Hence, the required formula for the lens is given as
Note:Before finding the lens formula, we must remember the sign convention for the lens, which is
(i) All distances are to be measured from the optical center of the lens.
(ii) Distances measured in the direction of incident ray (which is from left to right) are taken as positive.
(iii) Distances measured in the direction opposite to incident ray are taken as negative.
(vi) Height measured upward; the principal axis is taken as positive.
(v) Height measured downward; the principal axis is taken as negative.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Derive an expression for electric potential at point class 12 physics CBSE

Who discovered the cell and how class 12 biology CBSE
