Given:
- Focal length of convex lens, f = 30 cm
- Magnification of the real image, M = 5

To Find:
Object distance, u

Solution:
The magnification formula for a lens is given by:
M = -v/u

Where,
- M is the magnification
- v is the image distance
- u is the object distance

Step 1: Find the image distance
Given that the magnification is 5, we can rewrite the magnification formula as:
5 = -v/u

Step 2: Find the focal length of the lens
The focal length (f) of the lens is given as 30 cm.

Step 3: Use the lens formula to find the image distance
The lens formula is given by:
1/f = 1/v - 1/u

Since we are given the focal length (f) and we need to find the image distance (v), we can rearrange the formula as:
1/v = 1/f - 1/u

Substituting the values, we get:
1/v = 1/30 - 1/u

Step 4: Substitute the image distance in the magnification formula
Substituting the value of 1/v from step 3 in the magnification formula, we get:
5 = -1/u * (1/30 - 1/u)

Simplifying the equation, we get:
5 = -1/30 + u/u^2

Multiplying through by 30u^2 to eliminate the denominators, we get:
150u^2 = -u^2 + 30u

Simplifying further, we get:
151u^2 - 30u = 0

Step 5: Solve the quadratic equation
Factoring the equation, we get:
u(151u - 30) = 0

Setting each factor equal to zero, we get:
u = 0 or u = 30/151

Since the object distance cannot be zero, we discard the solution u = 0.

Therefore, the object distance is u = 30/151.

Step 6: Convert the answer to centimeters
To convert the object distance to centimeters, we multiply by 100:
u = (30/151) * 100
u = 19.87 cm (approx)

Final Answer:
The object distance is approximately 19.87 cm, which is closest to option A (36 cm).

Given:

1. Magnification (m) for real image = -5 (it's negative because real images are inverted)
2. Focal length (f) = 30 cm (assuming it's positive for a convex lens)

The lens formula relates the object distance (u), the image distance (v), and the focal length (f):

1/v + 1/u = 1/f

The magnification for a lens is given by:

m = -v/u

From the given data, m = -5, so:

v = 5u

Plugging this into the lens formula:

1/(5u) + 1/u = 1/30
Multiplying everything by 30u to clear the denominators:

6 + 30 = u
u = -36 cm

So, the object distance is 36 cm in front of the lens (the negative sign indicates the direction is opposite to the direction of incident light, which is conventional).