With the continuous advancement of infrared thermal imaging detection and guidance technologies, research on infrared radiation has become pivotal for mitigating threats to ships. The exhaust plume is one of the main sources of infrared radiation, the suppression of the plume is critical for the overall infrared stealth characteristic of ships. Experimental investigations serve as the principal means for understanding the infrared radiative characteristics of ship exhaust plumes and are important for the design and optimization of exhaust systems. In practical applications, experimental systems are often scaled down to reduce testing costs. Consequently, examining the similarity in infrared radiative characteristics between scaled and full-scale systems provides a foundation for applying experimental results. Existing studies mainly consider the similarity of temperature and concentration fields as prerequisites for achieving radiative similarity. However, whether optical thickness should remain consistent before and after scaling remains unresolved. In practical scaled model experiments, when the exhaust gas composition is consistent across scaled and full-scale systems, variations in geometric dimensions often result in changes to optical thickness. Exploring the impact of optical thickness on radiative similarity is therefore of significant academic and practical importance for validating and applying the results of scaled model experiments.Radiative similarity is investigated firstly in one-dimensional media. The analytical solution for radiative intensity is derived through solving the radiative transfer equation. Single-layer media with only high temperature gas and multi-layer media containing high temperature and surrounding low temperature gases are considered. Similarity conditions including consistent temperature and medium concentration distribution as well as equal optical thickness are examined. In order to check the applicability of the radiative similarity rules in a practical system, the plume of a ship exhaust system is investigated. Computational fluid daynamic are conducted to obtain the temperature field and the molar fraction fields of CO₂ and H₂O in the plume. The reverse Monte Carlo method is then employed to compute the radiative intensity of the exhaust system. This approach enables a detailed analysis of the infrared radiative similarity of different scaled models under actual exhaust conditions.For one-dimensional media, under the condition of the same temperature and gas concentration distribution as well as equal optical thickness, the maximum deviation between scaled and full-scale systems is 1.37%, regardless of whether the medium consists of a single layer or multiple layers of gas. When the gas concentration remains unchanged (resulting in significant variations in optical thickness), the infrared radiative intensity exhibits some differences between scaled and full-scale systems. For two-layer and three-layer media where there is a low temperature surrounding media, the deviation is less than 10%. The spectral distributions are illustrated in Fig.2 and Fig.3, while the results of the spectrally integrated radiative intensity are summarized in Tab.1. For the plume of a ship exhaust system, the infrared images are shown in Fig.9. Radiative intensity results in Tab.3 show that if the optical thickness is the same for scaled and full-scale systems, the biggest deviation is 2.15%. If the Mole fractions of the gases keep unchanged (with optical thickness changed), the biggest deviation is 10.47%.Under the conditions of consistent temperature distribution and similar flow fields as well as the same optical thickness, the scaled and full-scale exhaust systems exhibit high similarity in their infrared radiation characteristics. The integrated radiative intensity of the exhaust plume area is proportional to the square of the scaling ratio. When the scaled and full-scale systems satisfy similar temperature and flow fields but maintain a constant Mole fraction of the gas medium (resulting in changes in optical thickness), deviations in infrared radiation intensity are observed. Nevertheless, the results from the scaled model remain valuable for predicting the infrared radiation characteristics of the full-scale system. In scaled experiments of exhaust system, ensuring similar temperature and flow fields is crucial for maintaining radiation similarity. Although changes in optical thickness introduce some impact on radiative similarity, the deviations are relatively small and do not undermine the predictive value of the scaled model results.