Physics - Unit & Dimension Question with Solution | TestHub

Visual angle $\theta =1.8^{\circ }$

Distance from the eye $D=1$ m

We need to find the height of the object $h$ in cm.

First, convert the angle from degrees to radians:

$$1^{\circ }=\frac{\pi }{180}radians$$

$$\theta =1.8^{\circ }\times \frac{\pi }{180}=\frac{1.8\pi }{180}radians$$

For small angles, we can use the approximation $\tan \theta \approx \theta$ (in radians).

The relationship between the height of the object $h$, the distance $D$, and the angle $\theta$ is given by:

$$\tan \theta =\frac{h}{D}$$

Since $\theta$ is small, we can write:

$$\theta \approx \frac{h}{D}$$

Therefore,

$$h=D\theta$$

Substitute the values:

$$h=(1m)\times \left(\frac{1.8\pi }{180}\right)radians$$

$$h=1\times \frac{1.8\times 3.14159}{180}m$$

$$h\approx 0.0314159m$$

Convert the height to centimeters:

$$h=0.0314159m\times 100\frac{cm}{m}$$

$$h\approx 3.14cm$$

The approximate height of the object is 3.14 cm.

The final answer is $\boxed{3.14}$.