Lens Formula

Consider about a convex lens. O is the optical centre. AB is an object placed on the principle axis. The image A'B' is formed on the principle axis due to refraction of light. 

Mathematical Calculation 

Consider about the ∆ABO and ∆A'B'O.

Both triangles are similar.

AB/A'B' = OB/OB'   ....... (I)

Again, consider about the ∆MOF₂ and A'B'F₂

Both triangles are similar.

MO/A'B' = OF₂/B'F₂ ....... (ii)

From figure it is clear that

AB = MO

OB = -u

OB' = v

OF₂ = f

Form of equation no (ii) will be

AB/A'B' = OF₂/B'F₂ ...... (iii)

Now, from equation no (i) and (iii)

OB/OB' = OF₂/B'F₂

Now, putting the values of        OB = -u OB' = v OF₂ = f B'F₂ = v - f

-u/v = f/v - f

or, -uv + uf = vf

or, uf - vf = uv

Now, dividing both sides by uvf.

1/v - 1/u = 1/f

This is the lens formula.

Derivation of Lens Formula (Video Lecture)

 

6. Life Processes

 6. Life Processes
Questions - Answers
NCERT Textbook
Class 10
Science

1.1 What are life processes ?
Q.No. 1. Why is diffusion insufficient to oxygen requirements of multi-cellular organisms like humans ?
Answer
In multi-cellular organism, all the cells may not be in direct contact with the surrounding environment.
Thus, simple diffusion will not meet the requirements of all the cells.


Q.No.2. What criteria do we use to decide whether something is alive ?
Answer
Living creatures must keep repairing and maintaining their structures. Since all these structures are made up of molecules, they must move molecules around all times.
So, movement of various types can be taken as an indication of life.


Q.No.3. What are outside raw materials used for by an organism ?
Answer
Carbon based raw materials are used for by an organism to prevent damages and break-down of its structure.
Since life on earth depends on carbon based molecules, most food sources are carbon based.

Q.No. 4. What processes would you consider essential for maintaining life ?
Answer
Following process will be consider essential for maintaining life which are as follows.
1. Nutrition
2. Respiration
3. Transportation
4. Excretion