Test: Lense Formula - Class 10 MCQ

- To find the magnification of a lens, use the formula: Magnification (M) = Image distance (V) / Object distance (U).
- In this case, the object distance (U) is -9 cm (the negative sign indicates the object is on the same side as the incoming light). and the image distance (V) is 36 cm.
- Plugging in the values: M = 36 cm / - 9 cm = - 4.
- Negative sign that indicates the image is inverted but the magnitude is 4.

We know, height of the object is 4 cm h1, height of the image is 3 cm, h2. 
So we have, m = h2/h1 
=> m = 3/4  
=> m = 0.75
Therefore, magnification of the lens is 0.75 

A convergent beam of light passes through a diverging lens with a focal length of 0.2 m and comes to focus 0.3 m behind the lens. We need to find the position where the beam would converge in the absence of the lens.

Given:

• Focal length of diverging lens, f = -0.2 m (negative because it's a diverging lens)
• Image distance, v = 0.3 m

Using the Lens Formula:

The lens formula is:

(1 / f) = (1 / v) - (1 / u)

Step-by-Step Solution:

(1 / -0.2) = (1 / 0.3) - (1 / u)

-5 = (10 / 3) - (1 / u)

(1 / u) = (10 / 3) + 5 = (10 + 15) / 3 = 25 / 3

u = 3 / 25 = 0.12 m

1. Substitute the values into the lens formula:
2. Simplify the fractions:
3. Rearrange the equation to isolate (1 / u):
4. Calculate u:

Answer:

(d) 0.12 m

Since, it is a diverging lens, that is, a concave lens, we have
u = -10 cm, v = -6.5 cm

1/v - 1/u 
1/f   =-1/u - 1/u
1/f   = - 2/u
 u=-2f
 u=-24 cm

Focal length= -20(as it is concave lens)
v= -15 (as concave lens always forms virtual and erect image on left of lens)
Putting these values in lens formula,
1/ -20 - 1/u = 1/ -15
-1/ u= 1/-15 + 1/20
-1/u = -4+3/60
-1/u = -1/60
-u = -60
[u =60]

An object should be placed between F₁ and 2 F₁ so as to obtain the image formation used in slide projector. This is because, the image has to be enlarged and has to form at a little larger distance from the projector.

Given : f = 10 cm , m = 2
v / u = 2
v = 2u 
v = 2u -------(1)
according to lens formula , 
1/v - 1/u = 1/f
1/v - 1/u = 1/10 --------(2)
substitute (1) in (2)
1/2u - 1/u = 1/10
1 - 2 / 2u = 1/10
-1 / 2u = 1/10
-10 = 2u
u = -10/2
u = -5 cm
Therfore object should be placed 5 cm away from the lens.