Question

While a moving picture is being screened, a boy introduced a glass slab of thickness 3 cm and refractive index 1.5 between the projector and the screen. In order to have a clear picture on the screen, the screen should be moved through a distance of
(1) 1 cm away
(2) 1 cm nearer
(3) 2 cm away
(4) 3 cm away

Answer 1

Answer on Question#38973 – Physics -- Optics

While a moving picture is being screened, a boy introduced a glass slab of thickness 3 cm and refractive index 1.5 between the projector and the screen. In order to have a clear picture on the screen, the screen should be moved through a distance of

(1) 1 cm away

(2) 1 cm nearer

(3) 2 cm away

(4) 3 cm away

Solution

$$d = 3 \text{ cm}$$ $$n = 1.5$$

If angles $\alpha, \beta$ are small we can use $\frac{1}{n} = \frac{\sin \alpha}{\sin \beta} \approx \frac{\tan \alpha}{\tan \beta} \approx \frac{\alpha}{\beta}$

We can find $I = d(\tan \alpha - \tan \beta) \cot \alpha = d\left(1 - \frac{\tan \alpha}{\tan \beta}\right) \approx d\left(1 - \frac{\alpha}{\beta}\right) = d\left(1 - \frac{1}{n}\right) = 1 \text{ cm}$

Answer:

(1) 1 cm away